In holographic projection, ringing artifacts and degradation appear when the speckle noise problem is solved based on the random phase-free method. In this paper, we present a fast method to suppress the ringing artifacts in random phase-free kinoforms. We first reduce the distance between the hologram plane and the focal plane, and keep the focal length of the convergence light unchanged in the random phase-free method. Next, the complex amplitude is modulated using a single spatial light modulator. Consequently, the ringing artifacts and speckle noise reduction in the reconstructed image can be achieved. At the same time, the computing speed can be increased with our proposed method. Numerical simulations and optical experiments have validated the feasibility of the proposed method.