A　new　framework　based　on　the　curved　Riemannian　manifold　is　proposed　to　calculate　the　numerical　solution　of　the　Lyapunov　matrix　equation　by　using　a　natural　gradient　descent　algorithm　and　taking　the　geodesic　distance　as　the　objective　function.　Moreover,　a　gradient　descent　algorithm　based　on　the　classical　Euclidean　distance　is　provided　to　compare　with　this　natural　gradient　descent　algorithm.　Furthermore,　the　behaviors　of　two　proposed　algorithms　and　the　conventional　modified　conjugate　gradient　algorithm　are　compared　and　demonstrated　by　two　simulation　examples.　By　comparison,　it　is　shown　that　the　convergence　speed　of　the　natural　gradient　descent　algorithm　is　faster　than　both　of　the　gradient　descent　algorithm　and　the　conventional　modified　conjugate　gradient　algorithm　in　solving　the　Lyapunov　equation.