Sensitivity analysis of coupled acoustic-structural systems under non-stationary random excitations is investigated in this paper. The combined method of direct differentiation method (DDM) and pseudo excitation method (PEM) in previous work is computationally expensive for problems with large-scale design variables. To circumvent this difficulty, a fast sensitivity analysis method integrating the adjoint variable method (AVM) and PEM for coupled acoustic-structural systems under non-stationary random excitations is proposed. In this framework, the sensitivity analysis of coupled systems subject to non-stationary random excitations is transformed into a sensitivity analysis under pseudo-transient excitations with the help of PEM. On this basis, the computing efficiency of random response sensitivity is improved directly by solving the adjoint equations involved in the AVM. Numerical examples fully demonstrate the accuracy and efficiency of the proposed method.