Did Columbus really never know he reached a new continent?

His round-trip routes were suspiciously perfect. For him to think it was actually India would have been a gross miscalculation of the planet's diameter. He must have at the very least allowed for the possibility that the land he discovered was, in fact, a separate continent: he did have an imagination.

As for him refusing stubbornly to admit it, he must have had pretty good reasons. He had a contract of sorts with his superiors to deliver a new route to India. Delivering something else may have been tantamount to voiding the agreement and everything that came with it: privileges, money, status, etc. He may not have wished to provide them with the loophole. What others said, and what his employers thought was not his concern: he stuck to his guns in order to force them to honor the deal.

That Columbus died thinking he hadn't reached a "New World" is one of the most widespread of myths....In 1492 he might've thought he reached Asia, but in 1498--during the Third Voyage--he recorded in his Journal what is quoted at the top of this page--that "I have come to believe that this is a mighty continent which was hitherto unknown."

He was talking of South America; he was at the mouth of the Orinoco River, today Venezuela.

Columbus also began referring to this continent as OTRO MUNDO--"other world" in Spanish. He couldn't have been alluding to Asia, which is part of the Eurasian landmass and known to Europeans for thousands of years.

ALSO, in records of his lawsuit with the Spanish Crown (through which he attempted to get a bigger cut of the wealth produced by his exploration), he says that he deserves more because before his voyages no one even knew of the lands he'd reached. Therefore he was NOT talking of Asia, of which again Europe long knew and to which Europeans had long gone overland: e.g., the Venetian Marco Polo and his father and uncle. Even the ancient Romans seem to have sent an embassy to China, in the reign of the Philosopher-Emperor Marcus Aurelius Antoninus, 161-180 CE. The said court records concerning Columbus are the "Book of Privileges," and his reference to the new lands is in Document 43.

Moreover, Columbus coined the name "Indias Occidentales"--"West Indies." He knew of the East Indies (lands which had long been known to Europe, and which the Portuguese under Vasco da Gama reached in 1498 by sailing in the opposite direction--eastward); he simply had realized that HIS Indies were in a different part of the world.

For sources, see Kirkpatrick Sale's THE CONQUEST OF PARADISE, 1992 (written for the 500th Anniversary of the First Voyage). No better book on Columbus.

I think this question is conflating two things: whether Columbus thought he had found the Indies, and whether he thought he might have also discovered a new continent.

1. Did Columbus think for the rest of his life he had sailed to the Indies¹?

Yes he did.

Columbus appears to have been one of those people who believes things that they want to be true, and then go out looking for facts to back them up. What has sometimes been called The Unscientific Method. In his case, he wanted to believe the (East) Indies were nearby, so he went out and found the largest estimate of the size of Asia, paired it with his own personal miscalculated small estimate of the size of the Earth², and came up with a "scientifically backed" figure of 3,700 km to Japan. The true distance is more than 3 times that.

Even in the 15th Century, this was considered shaky logic, and he was laughed out of every nautical capital in Europe. It was only the news of Dias having discovered the way around Africa in 1488 that persuaded the neighboring Spaniards to take a chance on the nutjob.

So if Columbus had been the kind of guy who could get diverted from this belief by little things like the preponderance of evidence, or everyone else thinking otherwise, he would never have made his first voyage.

2. Did Columbus think he had found a new continent?

Quite possibly. The area south and west of the Indies was not well explored (by Europeans), and it was thought by many that there ought to be an other continent down there because there was so much more land known north of the Equator. Many people for the next couple of centuries even speculatively put it on their maps.

So in Columbus' world view, another continent West of "the Indies" could easily be explained as Terra Australis. Later European explorers who really did go to the East Indies and found landmasses in that region assumed exactly that. This is how Australia got its name.

Here's one such map from about 50 years later. Notice that just about all of the unexplored area in the South of the projection was filled with land rather than sea.

^{1 - This is the area we today call "Indonesia", although he mistakenly thought Japan was down there too. Because that would have made them even closer.}

^{2 - He took an Arab Astronomer's estimate of the size of the earth, but applied shorter Roman miles to it rather than the Arab miles the Astronomer was using. This error was likely pointed out to Columbus on multiple occasions (eg: the occasions he was rejected).}