In this paper, a new $L^2$ projection method is proposed for the optimal control of Navier-Stokes equations. The continuous equal-order conforming elements is employed. The method not only overcomes the spurious oscillations due to dominant convection, but also is stable for the equal-order combination of discrete velocity and pressure spaces by adding two local or global $L^2$ projection terms. Specially, a main advantage of the proposed method is that all the computations are performed at the same element level, without the need of nested meshes or the projection of the gradient of velocity/pressure onto a coarse level. The stability of the new method is given. For the state, adjoint state and control variables, the a priori error estimates are obtained uniformly with Reynolds number.
