The answer is "it depends".
The intrepid traveller is going to be traversing some of the most rugged terrain on earth, passing through modern day Afghanistan and the Himalayan mountains. Since maps as we know them are very rare, and generally inaccurate, he will have a difficult time finding the passes that lead through the mountains, and if he does find the pass, could end up heading into the Gobi Desert or some similarly inhospitable terrain.
Outside of the physical dangers, there are also hostile tribes to navigate past, language barriers and the usual bands of brigands and robbers out for a bit of sport at the expense of the traveller. As well, without skill or the knowledge of the various languages, he will have a tough time getting food, water, shelter either by asking for help or being able to trade with people.
Now this actually brings us to the answer: our intrepid traveller can get there by hooking up with one of the offshoots of the "Silk Road" that passed through central Asia from China to the Middle East. People had been sending caravans through these routes for centuries, but we are talking about large expeditions with ample supplies, pack animals, guards, trade goods and contacts with local potentates, warlords and priests to smooth the waters and get guides to show the way to the next way point. IF he has some sort of skill the Silk Road traders can use, or can pay for passage, then he doesn't have to walk at all.
While the Silk Road stretches over 6000km, the distance you are talking about is roughly half that, so a well organized expedition which is not making prolonged stops during their travels to trade, and isn't waylaid by bandits ( a real issue in the time period you are talking about, this is near the end of the time of Silk Road as a major trade route) should be about 75 days (assuming a mounted party can average @ 40 km a day). Obviously there will be periods where the convoy will be going far slower, but also once they reach China and the ground is relatively flat and they can move on well maintained and patrolled roads, then the pace will be much faster.
Bring a copy of the Lonely Planet guidebook and enjoy the trip.