In this paper, a one-dimensional mathematical model is established and simulated numerically for the interior ballistic cycle of two-stage light-gas launching facility with a piston-compressor type. A 35mm/130mm light-gas launcher is taken for the primary computing model, and lots of data, such as the pressure on light-gas chamber, the piston velocity, the diaphragm failure pressure, etc. are obtained by computing the model using the numerical difference scheme with the second order of numerical accuracy in space and the first order in time. On the basis of the results of analyzing these data systematically, some advices on enhancing the launching performance of light-gas launcher are put forward. The numerical results show that the developed mathematical model gives the correct trend and can provide useful calculated parameters for the structural design of the components of two-stage light-gas launcher.