A model of a pyrolysis gasifier, which is mainly composed of a pyrolysis, a cracking and a combustion chamber, is developed to predict its performance parameters and to simulate its operation. The model consists of a pyrolysis-cracking sub-model, a secondary gasification sub-model and a combustion sub-model, of which the pyrolysis-cracking sub-model is modified to predict components of the pyrolysis gas, Then, it with the other two sub-models can predict components, heating value and flow rate of the produced gas, thermal efficiency and total energy efficiency of the gasifier as well. Crank-Nicolson Scheme (half implicit difference formulation), in which the time step is not confined by stability and the cutting error is small, is applied to solving the model whose differential equations are nonlinear and have no analytic solution. Then, the nonlinear difference algebraic equations are solved by interations, which requires less storage of computer, Underrelaxation is applied to avoiding divergence of Causs-Seidel interations. Finally, the simulated results are input to Software Lotus 1-2-3, by which the results are printed and graphed so as to compare with the experimental ones, and it shows acceptable agreement, thus validate the model.