Structural comparison of multiple-chain protein complexes is essential in many studies of protein–protein interactions. We develop a new algorithm, MM-align, for sequence-independent alignment of protein complex structures. The algorithm is built on a heuristic iteration of a modified Needleman–Wunsch dynamic programming (DP) algorithm, with the alignment score specified by the inter-complex residue distances. The multiple chains in each complex are first joined, in every possible order, and then simultaneously aligned with cross-chain alignments prevented. The alignments of interface residues are enhanced by an interface-specific weighting factor. MM-align is tested on a large-scale benchmark set of 205 × 3897 non-homologous multiple-chain complex pairs. Compared with a naïve extension of the monomer alignment program of TM-align, the alignment accuracy of MM-align is significantly higher as judged by the average TM-score of the physically-aligned residues. MM-align is about two times faster than TM-align because of omitting the cross-alignment zone of the DP matrix. It also shows that the enhanced alignment of the interfaces helps in identifying biologically relevant protein complex pairs.