Solve the target search problems for unmanned aerial vehicle (UAV) swarm in uncertain environments without prior knowledge, this article designed a communication-constrained coverage search model and a new optimization algorithm. We proposed a multiobjective optimization model based on grid environment modeling and UAVs' modeling with communication constraints. Meanwhile, to optimize the proposed model, this article designed a collaborative search scheme based on model predictive control and communication constraints (CSS-MPCCCs) to solve the UAVs' path planning and decision-making at each moment. CSS-MPCCC is a two-stage optimization method with joint optimization of search performance and optimal selection from Parato frontier, which relies on NSGA-II. Our model and algorithm enabled the UAV swarm to perform coverage search on both static and dynamic targets. In simulations, the proposed CSS-MPCCC algorithm is compared with classical random search and parallel search algorithms, and the performance of model and algorithm is analyzed in several groups of simulations. It is validated that the proposed algorithm effectively enables the UAV swarm to search for static and dynamic targets in uncertain scenarios. © 2001-2012 IEEE.