A backward wave oscillator with parallel multiple beams and multi-pin slow-wave structure (SWS) operating at the frequency above 500 GHz is studied. Both the cold-cavity dispersion characteristics and CST Particle Studio simulation results reveal that there are obvious mode competition problems in this kind of terahertz source. Considering that the structure of the multi-pin SWS is similar to that of two-dimensional photonic crystals, we introduce the defects of photonic crystal with the property of filtering into the SWS to suppress high-order modes. Furthermore, a detailed study of the effect of suppressing higher-order modes is carried out in the process of changing location and arrangement pattern of the point defects. The stable, single-mode operation of the terahertz source is realized. The simulation results show that the ratio of the output peak power of the higher-order modes to that of the fundamental mode is less than 1.9%. Also, the source can provide the output peak power of 44.8 mW at the frequency of 502.2 GHz in the case of low beam voltage of 4.7 kV.