Functions with low c-differential uniformity have optimal resistance to some types of differential cryptanalysis. In this paper, we investigate the c-differential uniformity of power functions over finite fields. Based on some known almost perfect nonlinear functions, we present several classes of power functions $f(x)=x^d$ with $_{c}Δ_f\leq3$. Especially, two new classes of perfect c-nonlinear power functions are proposed.