This paper suggested a novel solution for the non-linear vibration equation of a pendulum. From the relevant differential equation and the initial condition for the problem, there are some derivative properties, which include the maximum displacement, the maximum velocity, the initial acceleration and the trajectory on the phase plane. The studied approximation motion for a pendulum was expressed in the form of Fourier series, in which the circular frequency was also an undetermined value. Let the approximate motion to be close to those derivative properties, the involved Fourier coefficients as well as the circular frequency can be evaluated, in which the four-parameter method and fiveparameter method are used. It is found that the results obtained from the fourparameter method have a high accuracy, and that the results obtained from fiveparameter method has a very high accuracy．