The universal design method of the Fourier series follower cam has a narrow application range to solve the near-rest interval and poor iterative convergence. In this work, an improved extensible near-rest angle high-speed Fourier cam design method is proposed. With the introduction of the function of angles in the near-rest interval, the general near-rest displacement equation of Fourier cam is solved. The velocity, acceleration equation, jerk, and jump of the follower are solved by successive derivation. Based on the cam feature parameters and profile curve data, the Fourier cam 3D model was established. The improved Fourier cam design method is verified by comparing it with the universal algorithm. The camshaft speed and push rod lift affecting the kinematic characteristic of the cam are investigated. The results indicate that the proposed model has a wide range of applications, excellent iterative convergence to solve the cam profile，and a small impact force. As the near-rest interval, camshaft speed, and push rod lift increase, the maximal velocity and acceleration of the follower increase. The proposed model is of guiding significance to reduce the vibration of the high-speed cam mechanism and improve the working precision of transmission.