The higher moments of GARCH models are of great importance in asset pricing and risk management. An efficient approach for calculating the higher moments of GARCH models is of great interest to both academic researchers and practitioners. This paper investigates the higher moments of GARCH models with a general form and obtains the analytical formulas. A nice property with our method is that we do not have to assume the distribution of the asset return as it is totally data-driven. We first introduce the model, and then present the formulas for calculating the higher moments of this model. Both simulation analysis and empirical evidence are used to evaluate the performance of our approach, and the results confirm its efficiency and accuracy.