As a competitive recovery method for heavy oil, In-Situ Combustion (ISC) shows its great potential accompanied by technological advances in recent years. Reservoir simulation plays an indispensable role in the prediction of the implementation of ISC projects. With the computational complexity, it is imperative to develop an effective and robust parallel in-situ combustion simulator. In this paper, a mathematical model for ISC is proposed, which takes full consideration of ISC related physical phenomena, including multi-dimensional multi-component three-phase flow, heat convection and conduction, chemical reactions, and mass transfer between phases. In the mathematical model, different governing equations and constraints are involved, forming a complicated PDE (partial differential equation) system. For physical and chemical behaviors, some special treatments for the ISC simulator are discussed and applied. Also, a modified PER (Pseudo-Equilibrium Ratio) method is proposed in this paper. A fully implicit scheme is applied, and discretization is implemented with the FDM(Finite DifferenceMethod). In solving nonlinear systems, the Newton Method is introduced, and both numerical and analytical Jacobian matrices are applied. Due to the complexity of an ISC problem, an appropriate decoupling method should be considered for which the Gauss-Jordan transformation is developed. Then, with certain preconditioners and iterative solvers, a numerical solution can be obtained. The results of different models are presented, which are validated with the results by CMG STARS. Also, the scalability of parallelization is shown, indicating the excellent performance of parallel computing. This accurate, efficient and parallel ISC simulator applies to complex reservoir models.