I'm a citizen of USA. My monthly net income is about $1500. Every month, I send $500-$800 U.S Dollars to my father and his family(my step-sister and step-mom) who are in China. All the transactions are sent through my Bank of America checking account. They are not U.S citizens. In case like this, is it possible to claim them as my dependents?

They may be eligible under "Qualifying Relative," and for this it is not necessary that they live with you. However, a dependent must be citizen or resident of the U.S.
Read: Your U.S. Tax Return: Requirements for claiming a dependent

Sorry, but in order to claim anyone OTHER than your spouse or child as a dependent, they MUST be in the U.S.

This is because you are from China. There are countries that, due to tax treaty, do NOT require the physical presence of the dependent, but China is NOT one of thoese countries.