I use a serum but my skin seems to become greasy quickly, am I doing something wrong?

I can't be entirely sure since you haven't told me how you're using it :/

Serum needs to be used UNDER moisturiser and only a tiny amount (just over a pea sized amount) for the entire face. Leave 10 minutes before applying a moisturiser too. It could be that you're using too much serum or you have oily/combination skin.
Try an oil free moisturiser too :)