Aiming at the shortcomings of solving eigenvalues and eigenvectors of matrix by using traditional methods, this paper proposes the population migration algorithm based on speed, which can convert solving matrix eigenvalue problem to unconstrained optimization problems, and take a population migration algorithm to solve matrix eigenvalues and eigenvectors. Simulation results show that the proposed method has higher solving precision, faster convergence and stronger stability, can effectively obtain eigenvalues and eigenvectors of general matrix.