The control problem of multi-UAV systems is studied based on differential game strategies.The goal is to minimize the performance metrics of each UAV.Under the open-loop Nash equilibrium condition，a finite-time cost function is introduced to transform the problem of multi-UAV system control into a linear quadratic differential game problem.Through coupled differential Riccati equations，optimal strategies under finite-time open-loop Nash equilibrium are derived，along with corresponding proofs.Subsequently，a method combining receding horizon with optimal control is employed，and the current state is taken as the initial condition for each time step，which achieves effective control of the multi-UAV system.Finally，simulation studies with five UAVs validated the effectiveness of the proposed method.