DC-DC switching converter is a time-variant and non-linear dynamic system, and it is difficult to analyze and design. The operating principles and four operating modes of Boost Zero-current-switch Quasi Resonant Converters (ZCS-QRCs) are analyzed. Its nonlinear model is built up based on time averaging Principle, illative process and the model built step are presented. The converter model is readily obtained by MATLAB, the waveforms of simulations of ZCS-QRCs Boost circuit models, mathematic models based on time averaging Principle of Quasi Resonant Converters are compared . At last, simulation results are verified and correspond to theory by comparing waveforms of simulations. Modeling Approach can be applicable other dc-dc Converter.