Discrimination between speech and music is important in many multimedia applications. Previously we proposed a new parameter for speech/music discrimination, the mean of minimum cepstral distances (MMCD), and it outperformed the conventional parameters. One weakness of MMCD is that its performance depends on range of candidate frames to compute the minimum cepstral distance, which requires the optimal selection of the range experimentally. In this paper, to alleviate the problem, we propose a multi-dimensional MMCD parameter which consists of multiple MMCDS with combination of different candidate frame ranges. Experimental results show that the multi-dimensional MMCD parameter yields an error rate reduction of 22.5% compared with the optimally chosen one-dimensional MMCD parameter.