Based on the dual mixed variational formulation for the Signorini problem,a nonconforming finite element method is proposed.The discrete B-B condition is confirmed and the error estimation O(h^3/4)for Raviart-Thomas(k=0)finite element is achieved.A Uzawa type algorithm is used for solving the Signorini problem which is discretized by conforming finite element method as well as nonconforming finite element method.The accuracy and efficiency of both are demonstrated by numerical results.By contrast to the conforming one,nonconforming method is more cost-effective.