This study investigates a numerical method for incompressible flows governed by unsteady Navier–Stokes equations, proposing a characteristic finite element method based on two Gauss integrations. The proposed method is compared and analyzed with the classical two-grid method and variational multiscale methods, respectively, with error estimates conducted. The superiority of the characteristic finite element method based on two Gauss integrations is verified through numerical examples with exact solutions. For a high Reynolds number of ${10}^6$, both algorithms remain stable. The computational results show strong agreement with those reported in well-established literature. Furthermore, simulations of the lid-driven cavity flow are performed, and the computational results are in excellent agreement with those of Ghia Ghia and Shin.