A new meshless numerical method for frictional contact problem is presented. In order to represent the discontinuous displacement field along contact surface and stress singularity around the contact surface tip

a discontinuous function and asymptotic crack tip displacement fields are added to the standard displacement formula based on the idea of partition of unity. Then

combined with frictional contact laws

a linear complementary model with the meshless method is formulated. In this approach

contact interface equations are discretized by contact point-discretization; and the global discretized system equation are transformed into a standard linear complementary problem that can be solved readily by using the Lemke method. Numerical examples show that the method is effective for solving the frictional contact problems.