In this paper, a discretization‐free approach based on the physics‐informed neural network (PINN) is proposed for solving the forward and inverse problems governed by the nonlinear convection‐diffusion‐reaction (CDR) systems. By embedding physical information described by the CDR system in the feedforward neural networks, PINN is trained to approximate the solution of the system without the need of labeled data. The good performance of PINN in solving the forward problem of the nonlinear CDR systems is verified by studying the problems of gas‐solid adsorption and autocatalytic reacting flow. For CDR systems with different Péclet number, PINN can largely eliminate the numerical diffusion and unphysical oscillations in traditional numerical methods caused by high Péclet number. Meanwhile, the PINN framework is implemented to solve the inverse problem of nonlinear CDR systems and the results show that the unknown parameters can be effectively recognized even with high noisy data. It is concluded that the established PINN algorithm has good accuracy, convergence, and robustness for both the forward and inverse problems of CDR systems.