Hyperbolic diffusion equation is a class of important partial differential equation in mathematics, and has been widely used in many engineering fields. It is usually used to describe the propagation of acoustic waves and currently in potential field, and also used to simulate the models of convection diffusion and heat conduction in computational fluid dynamics. In this paper, we propose a multiple integral finite volume method to solve the multiple problems of hyperbolic diffusion with dissipative terms. It is difficult to improve accuracy for solving this problem with classical finite volume method. Therefore, we propose a new finite volume format based on the variable limit integral, which improves the capability of traditional methods. We use the Fourier analysis method to analyze the stability of the discrete format, and provide the priori estimation as well as convergence. Finally, numerical experiments confirm the correctness of the proposed theoretical results.