In this paper, we use a phoxonic crystal (PxC) which can control the topological states of light and sound by breaking inversion symmetry and thus make it possible to achieve rainbow trapping of light and sound simultaneously. It is shown that topologically protected edge states can be obtained at the interfaces between PxCs with different topological phases. Thus, we designed a gradient structure to realize the topological rainbow trapping of light and sound by linearly modulating the structural parameter. In the proposed gradient structure, the edge states of light and sound modes with different frequencies are respectively trapped at different positions, owing to near zero group velocity. The topological rainbows of light and sound are simultaneously realized in one structure, which open a new, to the best of our knowledge, view and provide a feasible platform for the application of the topological optomechanical devices.