Abstract: Using continuous thought, an improved projection method that is fully high-order accurate in time for solving Navier-Stokes equations was constructed. The uniform mathematical description of this method was attained. Two projection algorithms with fully second- and third-order time accuracy were picked out. Numerical experiments about a 2D cavity driven flow and a Taylor vortex array solution were performed to validate the robustness and accuracy of the two algorithms respectively. In addition, atmospheric boundary layer with low turbulence was simulated by using these two algorithms. The simulation results were compared to prove the influence of algorithm’s time accuracy on the turbulence power spectrum of incompressible flow.