In this paper, the efficient recursive structure for computing arbitrary length M-dimensional (M-D) discrete cosine transform (DCT) is proposed. The M-D DCT are first converted into condensed one-dimensional DCT and discrete sine transform (DST) with a regular preprocess procedure. Using Chebyshev polynomials, the recursive filters for condensed 1-D DCT/DST are then derived to compute M-D DCT without involving any data transposition. The proposed structure requires fewer recursive loops than the traditional 1-D recursive structures, which are realized in M passes and (M-1) data transposition by the so-called row-column approach. With advantages of fewer recursive loops and no transposition memory, the proposed structures attain more accurate results and less power consumption than the existed ones, which are realized in the row-column approach. With regular and modular features, the proposed recursive M-D DCT structure is suitable for VLSI implementation.