The multi-reference interaction method is explicitly dependent on the electron-electron distance, and ACVQZ basis set is used in the <i>ab initio</i> calculation. The potential energy surface (PES) is fitted by using the permutation invariant polynomial neural network method based on 18222 <i>ab initio</i> points. In addition, the topographical features of the PES are compared with available theoretical and experimental data. The results indicate that the present PES is more accurate and can be applied to any type of dynamic study. In order to validate the PES, the dynamic study of the C<sup>+</sup> + H<sub>2</sub> → H + CH<sup>+</sup> reaction is carried out by using the quasi-classical trajectory method in a collision energy range of 0.4–1.0 eV. The integral cross sections and differential cross sections are calculated and compared with previous theoretical studies. For the integral cross section, the present results are, in general, in good agreement with previous theoretical studies, both of which increase with collision energy increasing. The forward and backward symmetric differential cross sections indicate that the “complex-forming” mechanism plays a dominant role in the reaction.