It seems the other guy has some kind of problem

Although I'm not totally with you, it seems the other guy has some kind of problem -- "同事给脸色看" is totally unacceptable and should not be tolerated. In any case like that, the management should intervene and give one of you a warning, if the warning does not work, then fire one of you or both of you.

If I were you, I would go straight and ask: "Is there any problem?", if he says yes, then ask "Does that problem have anything to do with me?", if he says yes, then get the management involved and go through the problem and get it straight. If he says no, then tell him "I do not want to see your bad mood at work wherever I'm involved, ok?" -- and you may or may not get the management involved, depends on how serious it is.