<p>The chemical master equation plays an important role in describing the time evolution of the probability of the number of reactants in a homogeneous chemical system. However, in complex systems, chemical reactions are often coupled with physical diffusion processes, which have a significant impact on the reaction dynamics, rendering the classical chemical master equation inadequate. Moreover, the reaction and diffusion processes are typically nonhomogeneous, further altering the time evolution of the chemical dynamic process. In this paper we propose a chemical continuous time random walks under anomalous diffusion model based on the renewal process where the waiting times are arbitrary distributed. By applying this model, we obtain the generalizations of the chemical diffusion master equation, the mass action laws, the fluctuation-dissipation theorem in the closed system, and the Gillespie algorithm to describe the effects of physical diffusion and the heterogeneity of the system. As an example, we analyze the monomolecular reaction-diffusion system with exponential and power-law waiting times, respectively, and show the fractional memory effect of the average of the concentrations of reactants on its history. This work gives one approach to describe anomalous diffusion with any reaction, and provides the systematic stochastic theory for modeling the heterogeneous chemical diffusive system.</p>