The generalized energy integral and Whittaker method of reduction for the dynamics system based on non-standard Lagrangians are studied. Firstly, in view of two kinds of non-standard Lagrangians, i.e., exponential Lagrangians and power law Lagrangians, the Hamilton action with non-standard Lagrangians is defined, and the Hamilton principles and the Lagrange equations of the system are obtained. Secondly, the condition under which the generalized energy integral with non-standard Lagrangians exists and the form of generalized energy integral are established by using the Lagrange equations of the system. Thirdly, the famous Whittaker method of reduction is extended, and the Whittaker equations for the dynamics system with non-standard Lagrangians are obtained. Finally, an example is given to illustrate the application of the results.