We propose and analyze a C0-weak Galerkin (WG) finite element method for the numerical solution of the Navier-Stokes equations goveing 2D stationary incompressible flows.Using a stream-function formulation,the system of Navier-Stokes equations is reduced to a single fourth-order nonlinear partial differential equation and the incompressibility constraint is automatically satisfied.The proposed method uses continuous piecewisepolynomial approximations of degree k + 2 for the stream-function ψ and discontinuous piecewise-polynomial approximations of degree k + 1 for the trace of ▽ψ on the interelement boundaries.The existence of a discrete solution is proved by means of a topological degree argument,while the uniqueness is obtained under a data smallness condition.An optimal error estimate is obtained in L2-norm,H1-norm and broken H2-norm.Numerical tests are presented to demonstrate the theoretical results.