In this paper, the Gauge-Uzawa method is applied to solve the Navier-Stokes equations with nonlinear slip boundary conditions whose variational formulation is a variational inequality
of the second kind with the Navier-Stokes operator. In , a multiplier was introduced such
that the variational inequality is equivalent to the variational identity. We give the Gauge-Uzawa
scheme to compute this variational identity and provide a finite element approximation for the
Gauge-Uzawa scheme. The stability of the Gauge-Uzawa scheme is showed. Finally, numerical
experiments are given, which confirm the theoretical analysis and demonstrate the efficiency of
the new method.