Abstract <p>The (2+1)-dimensional generalized Camassa–Holm Kadomtsev–Petviashvili equation is always used in tiny amplitude shallow water waves. In this study, we apply the CK direct method to seek new similarity reductions and new exact solutions of the g-CH-KP equation. As far as we know, no one has used the CK direct method to solve the g-CH-KP equation in the literature, presumably due to the complex and tedious calculations. Through the separation method, we mitigate the computational complexity and obtain new similarity reductions and new exact solutions. The results we obtained have two cases. In the first case, the g-CH-KP equation was reduced to some ordinary differential equations and some new similarity reductions are obtained, including Painlevé I, Painlevé IV similarity reductions and the Weierstrass elliptic function solution. In another case, new exact solutions are obtained, including the rational function solutions and hyperbolic soliton solutions. These exact solutions have not been previously reported, as far as we know. Physically, through the analysis of the new solutions, the hyperbolic soliton solutions reveal new physical phenomena in shallow water wave propagation governed by the CH-KP equation.</p>