We present an efficient technique for multi-frequency acoustic analysis by the variational indirect boundary element method. The system coefficient matrix of the boundary element method is frequency dependent and requires cumbersome computation in multi-frequency acoustic analysis. To eliminate the frequency dependency of a system coefficient matrix of the boundary element method, the free space Green's function is approximated using Taylor series. Unlike the existing Taylor series expansion method, the present technique deals with the approximated series of the Green's function using matrix decomposition and multiplication. For multi-frequency acoustic analysis, the coefficient matrix of the frequency independent system is calculated only at the first frequency; from the remaining frequencies, it is calculated as the product of the wave number matrix and the frequency independent coefficient matrix at the first frequency. The efficiency of the present technique is demonstrated through numerical examples. The results are compared with those of the conventional indirect method and the existing series expansion method by Wang.