Multiple unmanned aerial vehicle (Multi-UAV) cooperative area search is an important and effective means of intelligence acquisition and disaster rescue. Search path planning is a critical factor to improve multi-UAV search performance. Aiming at the search inefficiency resulting from insufficient cooperation between UAVs in existing researches, we present a novel distributed real-time search path planning method based on distributed model predictive control (DMPC) framework. Firstly, we formulate the overall search objective function in finite time domain, considering not only repeated searches, but also maintenance of connectivity and collision avoidance between UAVs. Secondly, we decompose the overall search objective function to establish a distributed constrained optimization problem (DCOP) model, so that all UAVs optimize the overall search objective by interacting with neighbors. Thirdly, aiming at the problem of falling into the local optima in existing algorithms, distributed stochastic algorithm based on enhanced genetic algorithm (DSA-EGA) is proposed to solve the established DCOP model. We design a point crossover operator and introduce anytime local search (ALS) framework that stores the global optimal solution explored. Finally, the simulation results of different benchmark problems demonstrate that the proposed DSA-EGA outperforms other state-of-the-art algorithms in terms of the quality of solution. The simulation results of cooperative area search problems illustrate that the established DCOP model improves the search efficiency by 7.7%, and DSA-EGA improves the search efficiency by 4.3% at least. In addition, we also verify that our method has high scalability.