Collaborative search in unknown areas is a fundamental task for unmanned aerial vehicles (UAV) in which the search plannings are basic problems that should be seriously concerned. Potential game is a past useful technique for the multi-UAV search decisions which is based on a cooperative game framework, however the possible conflicts between different UAVs under dense constraints may cause task failures due to the fast premature of search process. This paper presents a consensus-based potential game method (CBPG) for the multi-UAV collaborative search under dense flight constraints including the collision avoidances and the connectivity preservations. It takes an auction-based conflict resolution mechanism to keep the consistency between UAVs’ actions and thus could relieve the local optima dilemma and achieve efficient coverages. Simulation results show the advantages of the CBPG over traditional algorithms on the premature avoidances under dense flight constraints.