My advisor refuses to write me a recommendation for my PhD application unless I apply to his lab 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.