Direct digital synthesis (DDS) technology is widely used in navigation, communications, aerospace, and other fields. Due to the technical limitations in the process of DDS digitization, the output spectrum of DDS is inevitably spurious. In order to meet the requirement of the pure frequency reference signal for modern instrument or equipment, it is necessary to correctly analyze the spur of DDS and effectively suppress it. In this paper, the causes of the spur in traditional DDS are analyzed, and a piecewise linear approximation method is proposed to suppress the amplitude quantization spur of DDS. In order to verify the effectiveness of the proposed spurious suppression method in this paper, the MATLAB simulation is carried out and a field programmable gate array (FPGA) hardware platform for DDS is developed. The simulation and actual test results prove the feasibility of this method. In the limited storage space, this method improves the accuracy of amplitude quantization, reduces spurs, and enhances the accuracy of synthetic frequency.