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Persistent surveillance is one of the major tasks envisioned for unmanned aerial vehicles in that some regions of interest need to be continuously surveyed. This distinction from the one-time coverage/exploration does not allow a straightforward application of the most exploration techniques to address the persistent surveillance problem. This article introduces and demonstrates a method of alterable artificial potential field to control a group of unmanned aerial vehicles to stay over the region of interest. We present attractive potential field to drive the unmanned aerial vehicles to desirable areas, obstacle potential field to move away from obstacles, collision avoidance potential field to control unmanned aerial vehicles not to collide with others, and formation of potential field to make unmanned aerial vehicles gather in a group. The simulation results show that the proposed approach could generate collision-free path for unmanned aerial vehicles staying over the region of interest for a long endurance.