The dynamic analysis of wind turbine drive train is carried out in the present paper. Gear box dynamic modelling is challenging due to the complexity involved in mathematical formulation. The mathematical model is developed based on Lagrange's formulation. The aerodynamic torque which is applied as an external load is calculated from the empirical approach. The input wind fluctuation for simulation is modelled as an average magnitude of the wind which changes slowly in time and a sinusoidal variation of wind velocity is considered. The governing differential equations of motion are solved by an implicit Newmark time algorithm. The Eigen frequencies and Eigen vectors of the model are obtained. The responses of the system in time and frequency domain are also obtained.