Aiming at the path planning problem of unmanned aerial vehicle （UAV） with limited view ability in unknown environment， a particle swarm optimization （PSO） algorithm based on convex optimization is proposed to select path points. In the iterative optimization process， the fitness function of particle swarm is designed based on the trajectory， obstacle avoidance and the distance to the end point solved by the convex optimization. The trajectory between the path points is displayed after the optimal path point is obtained. The obtained trajectory is used as a part of simultaneous localization and mapping （SLAM） to build a more reliable environment map. Theoretical analysis and experimental simulation results show that compared with other intelligent algorithms and sample-based path planning algorithms， the proposed PSO based on convex optimization can effectively improve the efficiency of path planning and reduce the length of the planned path.