A high-speed cam design method is proposed based on the Fourier series and principle of Minimum Gaussian square difference. The design principle for the cam of the Fourier series follower motion law（ referred to as the Fourier series cam） and the construction of its displacement function are analyzed. Taking the flat-bottom centering setting push rod-cam mechanism as an example,the cam profile of the Fourier series cam is designed. A valve train including the cam mechanism is established,the natural vibration modes and motion features of the valve are analyzed to validate the work property of the cam. The results show that the displacement curve of the valve is determined by the profile of the cam within a certain range of rotation speeds.The maximum value of velocity of the valve will increase with the increase of the rotation speed of shaft and the increase of the valve clearance. The acceleration of valve will increase first and then decrease in the rise process and will have a symmetric trend in the return period.