A fast algorithm for computing the two-dimensional (2-D) forward and inverse modified discrete cosine transform (MDCT and IMDCT) is proposed. The algorithm converts the 2-D MDCT and IMDCT with block size M×N into four 2-D discrete cosine transforms (DCTs) with block size (M/4)×(N/4). It is based on an algorithm recently presented by Cho et al. [An optimized algorithm for computing the modified discrete cosine transform and its inverse transform, in: Proceedings of the IEEE TENCON, vol. A, 21–24 November 2004, pp. 626–628] for the efficient calculation of one-dimensional MDCT and IMDCT. Comparison of the computational complexity with the traditional row–column method shows that the proposed algorithm reduces significantly the number of arithmetic operations.