Abstract: S-box is important in symmetric cryptosystem.One method is proposed to constructed perfect nonlinear S-box over finite field.Compared to the construction over vector space，it is easier to study the properties of permutation polynomials，like algebraic degree.By choosing different parameters，different types of S-boxes can be constructed.For example，by choosing α^x as the permutation polynomial，we obtain the S-box once constructed by Satoh et al.By selecting permutation of form x^d，we obtain another type of S-boxes.The algebraic degree of any nonzero linear combination of its output functions is highest.