A kind of arc-linear permanent-magnet synchronous machine (AL-PMSM) used for scanning system, which requires high positioning accuracy, high response performance, and wide scanning range, is proposed and researched. Due to the finite length of stator core and rotor core, the AL-PMSM suffers from stator end effect and rotor end effect. The cogging torque caused by stator end effect can be reduced significantly by stator length optimization, PM shape optimization, and so on. The cogging torque caused by rotor end effect is mainly analyzed and reduced in this paper. The rotor end effect occurs when the rotor end region is close to the stator end region and the influence of rotor end effect is mainly two pole pitches. In order to reduce the cogging torque caused by rotor end effect, shape optimization of the edge permanent magnets, especially the first edge PM and second edge PM, is researched and compared. After optimization, the smooth scanning range is improved from ±47.8° to ±56.2° by 17.6% with the peak-to-peak value of cogging torque less than 0.19 Nm. The effectiveness of the optimization method is verified by the finite-element method.