Abstract: Starting pressure gradient exists in the low permeability reservoirs. The pressure can not be transimitted infinitely far away instantaneously, but the moving boundary expands outwards constantly. This paper puts forward a new pressure transient model to calculate the pressure of non-Newtonian power-law fluids with moving boundary in double porous media and fractal reservoir. By using Douglas-Jones predictor-corrector method, the paper obtains the numerical solution to the infinitely large system with constant production rate. The effects of the parameters on the pressure curves are discussed, such as the power-law exponent of the non-Newtonian power-law fluids, fractal parameters and double porous media parameters.