This study employed Lyapunov function method to investigate the stability of nonlinear ordinary differential equations. Using Lyapunov direct method, we constructed Lyapunov function to investigate the stability of sixth order nonlinear ordinary differential equations. We find $ V(x) $, a quadratic form, positive definite and $ U(x) $ which is also positive definite was chosen such that the derivative of $ V(x) $ with respect to time was equal to the negative value of $ U(x) $.