I got my master’s degree in China and had worked for two years as a visiting student in the US. Although my master thesis’s supervisor promised to write me a recommendation letter, my visiting student advisor refused. He is the corresponding author of all my publications. What's more, research experience in his lab was included in my personal statement. He said he would offer me a recommendation letter only if I apply for his lab. When I asked whether he could recommend me for other universities, he did not reply to my email. Is there any possibility that I get an offer without his reference letter? How should I explain this to an admission committee?
You will need to find another reference.
I recommend not keeping this supervisor up-to-date on your application status.
When asked why his reference was not included, probably you could just say factually and without sounding judgemental that the student advisor offered a reference only under condition that you would work for them, so you sought another reference [pretend that you do not realise what that means - coming from China, you can probably present it, if asked, as if you assume this may be the norm to only give out references under these conditions; of course, this is not true, but I think your best bet is to take the "naive" route].
You also have publications with this student advisor, so that already proves that your work is good enough to pass peer review - a direct reference from them would be nice, but is not anymore vital at this stage.
While not illegal, the behavior of your advisor is completely unethical. The behavior is so bad, that it can tarnish the reputation of an entire department. I suggest you attempt to get his position in writing. Make sure you clearly understand that he will recommend you for a position in his lab but no where else. Not recommending someone to a particular program, or even every program, is not unethical. Limiting letters for people to only places where you will benefit is unethical.
Once you have it in writing (or at least a clear understanding), you should approach your department chair asking for a letter of recommendation. Explain that your supervisor is willing to write a letter for his lab, but not for any other labs. Then show him the email. The department chair will also likely feel guilty and read over your papers and write a reasonable letter. More importantly, the department chair can explain why you don't have a letter from your supervisor (i.e., that the chair believes the supervisor is happy with your work, but refuses to write letters because he does not want to lose you). The chair will most likely then have a private discussion with the supervisor about his behavior.