The moving contact line model we consider is a sharp-interface model consisting of the two-phase incompressible Navier-Stokes/Stokes equations with the classic interface conditions, the Navier boundary condition for the slip velocity along the wall, and a contact line condition which relates the contact angle to the contact line velocity. We propose an efficient method for the model. The method combines a finite element method for the Naiver-Stokes/Stokes equations on the bulk mesh with a parametric finite element method for the dynamics of the fluid interface. In this method, the contact line condition is formulated as a time-dependent Robin-type boundary condition for the interface so it is naturally imposed in the weak form of the model. The numerical schemes enjoy a similar energy law as in the continuum model. Numerical examples are presented to demonstrate the convergence and accuracy of the numerical method.