Hi, I got an postdoctoral fellow offer under H1B visa from one university in US. If I hold Singapore passport, do I need to pay tax? How about china possport? Thanks.

You are under the wrong visa. H-1B visa is a work visa, which means you are liable for all taxes (Social Security, Medicare, income taxes at both federal and state level).

You might try a J-1 visa, which may allow you to be completely exempt from taxes if the fellowship is for only two years or less and you are using the fellowship for research.