The direct-drive type high-torque-density motor is one of the most promising solutions of electric propulsion for aircraft. The cogging torque of the direct-drive motor causes torque ripple, vibration, and noise, which seriously affect the stability and reliability of the electric propulsion system for aircraft. In this paper, a novel direct-drive type high-torque-density dual-rotor radial flux permanent magnet synchronous motor (DRPMSM) is proposed, and its cogging torque is weakened by permanent magnet shape design and pole-arc coefficient combination. An eccentric and chamfered permanent magnet shape is proposed, and the influence of eccentric distance and chamfer angle on cogging torque is clarified. Through the pole-arc coefficient combination design of the inner and outer rotors of the DRPMSM, the cogging torques of the inner and outer rotor are phase reversed, thus further reducing the total cogging torque of the DRPMSM. By employing the response surface method, a mathematical model is established for the cogging torque of the DRPMSM in relation to the pole-arc coefficients, chamfer angle, and eccentric distance of the permanent magnets. The parameters that minimize the cogging torque of the DRPMSM are obtained using a genetic algorithm. A prototype is manufactured according to the optimized parameters, and experimental results validate the correctness of the theoretical analysis and the effectiveness of the optimization design method.