A new noise reduction method for speech signals is proposed in this paper. The method is based upon the N-mode singular value decomposition algorithm, which exploits the multilinear subspace analysis of given speech data. Simulation results using both synthetically generated and real broadband noise components show that the enhancement quality obtained by the multilinear subspace analysis method in terms of both segmental gain and cepstral distance, as well as informal listening tests, is superior to that by a conventional nonlinear spectral subtraction method and the previously proposed approach based upon sliding subspace projection.