A control method based on variables substitution and matrix decomposition is proposed for group attitude coordinated control of multi-spacecraft with directed switching topologies. Firstly, the paper provides the properties of the eigenvalues of the Laplacian matrix. The variable in the spacecraft attitude model is substitued, which turns the group attitude coordinated control problem of a nonlinear system into the group consensus problem of a linear system, and then it is turned into the stability problem of a switched linear system by decomposing the Laplacian matrix. It is analyzed using the Lyapunov stability theory, and the results show the minimum dwell time is presented. Simulation is carried out on a system with two subgroups, and the results show that effectiveness of the proposed method.