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According to the assumption of slightly compressible fluid, the quadratic gradient term in the nonlinear partial differential equations for the traditional well-test model is usually neglected. The linear partial differential equation is thus established. It is known that neglecting the quadratic gradient term results in errors for long-time well tests. A nonlinear flow model for fractal medium is constructed and the quadratic gradient term is considered. The exact solutions of the fractal reservoir models are obtained by Laplace transform and Weber transform in a constant-rate and constant-pressure production for an infinitely large system. This paper addresses the variation of pressure with fluid compressibility coefficient and fractal reservoir parameters. The plots of the typical pressure curves are constructed, and the results can be applied to well-test analysis.