This paper focuses on the application of surveillance and monitoring using unmanned aerial vehicles (UAVs). A novel coverage model is proposed to characterize the quality of coverage (QoC) of a target by a UAV. On the basis of this model, a reactive collision free three-dimensional deployment algorithm is proposed, with the goal of maximizing the overall QoC of targets by a network of UAVs. The algorithm consists of two navigation laws for the horizontal movement and the vertical movement, both of which are easily implementable in real time. The convergence of the algorithm is proved, and the computational complexity is analyzed. Computer simulations are conducted to demonstrate the performance of the proposed method.