The use of Unmanned Aerial Vehicle (UAV) to continuously monitor designated areas can play a role in deterring invasion and damage as well as discovering abnormalities in time, but the fixed monitoring rules are easy to be discovered by the invaders. Therefore, it is necessary to design a random algorithm for UAV flight path. In view of the above problem, a UAV persistent monitoring path planning algorithm based on Value Function Iteration (VFI) was proposed. Firstly, the state of the monitoring target point was selected reasonably, and the remaining time of each monitoring node was analyzed. Secondly, the value function of the corresponding state of this monitoring target point was constructed by combining the reward/penalty benefit and the path security constraint. In the process of the VFI algorithm, the next node was selected randomly based on ε principle and roulette selection. Finally, with the goal that the growth of the value function of all states tends to be saturated, the UAV persistent monitoring path was solved. Simulation results show that the proposed algorithm has the obtained information entropy of 0.905 0, and the VFI running time of 0.363 7 s. Compared with the traditional Ant Colony Optimization (ACO), the proposed algorithm has the information entropy increased by 216%, and the running time decreased by 59%,both randomness and rapidity have been improved. It is verified that random UAV flight path is of great significance to improve the efficiency of persistent monitoring.