We present a superconvergent hybridizable discontinuous Galerkin method for the steady-state incompressible Navier–Stokes equations on general polyhedral meshes. For an arbitrary conforming polyhedral mesh, we use polynomials of degree , and to approximate the velocity, velocity gradient and pressure, respectively. In contrast, we use only polynomials of degree to approximate the numerical trace of the velocity on the interfaces. Since the numerical trace of the velocity field is the only globally coupled unknown, this scheme allows a very efficient implementation of the method. For the stationary case, and under the usual smallness condition for the source term, we prove that the method is well defined and that the global -norm of the error in each of the above-mentioned variables and the discrete -norm of the error in the velocity converge with order for . We also show that for , the global -norm of the error in velocity converges with order . From the point of view of degrees of freedom of the globally coupled unknown (numerical trace), this method achieves optimal convergence for all the above-mentioned variables in the -norm for , superconvergence for velocity in the discrete -norm without postprocessing for and superconvergence for velocity in the -norm without postprocessing for .