The refraction and scattering of nonlinear acoustic waves play an important role in the realistic application of medical ultrasound. One cause of these effects is the tissue dependence of the nonlinear medium behavior. A method that is able to model those effects is essential for the design of transducers for novel ultrasound modalities. Starting from the Westervelt equation, nonlinear pressure wave fields can be modeled via a contrast source formulation, as has been done with the INCS method. An extension of this method will be presented that can handle inhomogeneities in the coefficient of nonlinearity. The contrast source formulation results in an integral equation, which is solved iteratively using a Neumann scheme. The convergence of this scheme has been investigatedfor relevant media (e.g., blood, brain, and liver). Further, as an example, the method has been applied to compute the 1D nonlinear acoustic wave field in an inhomogeneous medium insonified by a 1 MHz Gaussian pulse propagatingup to 100 mm. The results show that the method is able to predict the propagation and the scattering effects of nonlinear acoustic waves in media with inhomogeneities in the coefficient of nonlinearity. This motivates a similar extension ofthe 3D INCS method.