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• Topological acoustic rainbow trapping can be realized by regulating topological edge mode dispersion curve and group velocity. • The topological phononic crystal is robust to multiple structural disorders, such as scaling, rotating and removing unit cells. • The proposed gradient phononic crystal is capable of recovering the Gaussian pulse signal from the background noise. In this letter, a gradient phononic crystal (PC) structure is proposed for robust enhanced acoustic sensing. At first, the topologically protected edge states are introduced by breaking the space-inversion symmetry of the PC structure. Then, the topological edge mode dispersion curve and group velocity are demonstrated to be regulated by varying the structure parameters gradually and the edge states can be slowed down to zero group velocity and trapped at different positions. Consequently, topological acoustic rainbow trapping is formed. Furthermore, the robustness and enhancement properties are verified both numerically and experimentally. All the results indicate that the gradient PC structure is able to realize robust enhanced acoustic sensing. This work opens a new vista to improve the robustness of the PC-based enhanced acoustic sensing. [ABSTRACT FROM AUTHOR]