Abstract: A new approach was proposed based on the Log-Euclidean metric to solve the Lyapunov equation. First, the origin of Lyapunov equation was introduced. Then the Riemannian metrics on a manifold of symmetric positive definite matrices and the geodesic distance function under Log-Euclidean metric were presented. Last, the iterative formula for the solution to Lyapunov equation was obtained, and some simulation results were shown.