Fast prediction of injection pressure and minimal front temperature can usually he used to optimize the process parameters for injection moulding. In this paper, a fast strip analysis (FSA) model was presented on the basis of a geometric approximation method, which simplifies an original part to a rectangular edge-gated strip. The dimensions of the rectangular strip were calculated through the original part's geometric mesh by using graph theory. Subsequently, a finite difference method was employed to simulate a non-isothermal and unidirectional flow in the strip. Numerical examples show that although FSA model is an approximation method, its results are approximately identical to that of detailed CAE software, while the running time of the proposed model is several magnitudes less than that of CAE software.