Perfect nonlinear function is the optimal function on finite fields with odd character that can resist differential cryptanalysis. All the six classes of the already known perfect functions currently are 2-1. This study proved that when is Dembowski-Ostrom function or Coulter-Matthews function on , the preimage distribution of the perfect nonlinear function has just two kinds of values, one corresponds to all the elements of quadratic residual on , and the other kind corresponds to all the non quadratic residual on .