This paper presents a mathematical model for the topological optimization of multi-material structures under inertial load based on the guide-weight method， which aims to minimize structural compliance while adhering to volume constraints. The topological optimization problem of multi-material structures is decomposed into topological optimization problems of single-material structures. Rational approximation of material properties （RAMP） was used to express the nonlinear relationship between density and elastic modulus. The guide-weight method was employed to develop iterative expressions for design variables under inertial loads. Numerical examples demonstrate the effectiveness of this approach in optimizing multi-material structures under inertial loads. The results show that the RAMP interpolation method produces clearer topology configurations with fewer gray units and reduces structural compliance （up to 35.2% in example 1） compared with other general interpolation models. The greater the influence of inertial load on the design area， the higher the elastic modulus of distributed material. A high ratio of modulus to density can significantly increase the stiffness of a structure.