Yes, you absolutely can.  However, you should go very slowly because if you're not careful your hair might get stuck in between the blades and that will cause some serious problems. If you're using an AC model of any sort then there shouldn't be any problems with using a trimmer on curly hair. If you're using a battery-powered trimmer, then the blades might overheat because of the curly hair.  In that case, it would be better to use a cordless trimmer so there isn't any overheating problem at all.