A projection scheme for the numerical solution of the incompressible Navier-Stokes equations is presented. Finite element discontinuous Galerkin (dG) discretization for the velocity in the momentum equations is employed. The incompressibility constraint is enforced by numerically solving the Poisson equation for the pressure by using a continuous Galerkin (cG) discretization. The main advantage of the method is that it does not require the velocity and pressure approximation spaces to satisfy the usual inf-sup condition, thus equal order finite element approximations for both velocity and pressure can be used. Furthermore, by using cG discretization for the Poisson equation, no auxiliary equations are needed as it is required for dG approximations of second order derivatives. In order to enable large time steps for time marching to steady-state and time evolving problems, implicit schemes are used in connection with high order implicit RK methods. Numerical tests demonstrate that the overall scheme is accurate and computationally efficient.