A path planning algorithm based on multi-objective particle swarm optimization (MOPSO) is proposed to plan the puncture path of bevel-tip flexible needles from the start point to the target in a complex environment. The flexible needle kinematic model in soft tissues is analyzed, and the relationship between the puncture path and controlled variables is established. Then a mathematical description of obstacles is built based on the constraint conditions of obstacles. After that, the path planning problem is transformed into a multi-objective optimization problem whose optimization objectives include puncture error, puncture danger and puncture length according to the clinical requirements of puncture. Thus, a mathematical model of the multi-objective optimization problem is set up, and MOPSO algorithm is employed to solve the multi-objective optimization problem. Finally, simulations are performed to demonstrate the effectiveness of the proposed method, and the online modification of puncture paths is analyzed.