The mission planning problem in command and control organization can be mapped into a combinatorial optimization problem with many variables and is difficult to solve. The traditional heuristic list planning method faces the problems of high time complexity and poor real-time response. For the mission planning problem in command and control organization, a quantum circuit solution scheme is proposed based on quantum approximate optimization algorithm in this work. Firstly, the mission planning problem is transformed into a typical combinatorial optimization problem, the exact coverage problem. Then, by constructing the corresponding mathematical model, the final state Hamiltonian expression of the quantum approximate optimization algorithm for the exact coverage problem is derived. The quantum circuit based on the quantum approximate optimization algorithm is designed. Finally the parameters in the quantum logic gate are optimized by the momentum gradient descent algorithm, and the simulation experiment is carried out by using the quantum software development environment of the Origin Quantum Computing Company. The simulation results show that the quantum circuit scheme can be used to solve the mission planning problem, reduce the time complexity of the algorithm, and improve the resource utilization to a certain extent. This work lays the foundation for further application of quantum algorithm to solving the mission planning problem in command and control organization.