In the battlefield environment, a relay communication chain is urgently needed to be formed between two nodes which are unable to communicate. In this paper, Unmanned Aerial Vehicles (UAVs) are used as relay nodes, and a model for relay node placement is given. The objective functions are the minimum number of required relay UAVs and the minimum time cost for forming the relay chain, and the constraints are the safety of UAVs and the effectiveness of the relay chain. Since the problem is mixed integer multi-objective optimization which is known hard to be solved, and the requirement for quick and effective decision is urgently needed, a Polynomial Time Relay Placement Algorithm (PTRPA) is given to solve the problem fast and provide a sub-optimal solution. The feasibility and effectiveness of the algorithm is validated with simulation, and the impacts of different factors on the algorithm is studied with the Monte-Carlo method. The research figures out a new relay node placement scenario in the coming networked warfare, and provides a referable modeling and solving method.