This paper investigates the problem of speaker recognition in noisy conditions. A new approach called nonnegative tensor principal component analysis (NTPCA) with sparse constraint is proposed for speech feature extraction. We encode speech as a general higher-order tensor in order to extract discriminative features in spectrotemporal domain. Firstly, speech signals are represented by cochlear feature based on frequency selectivity characteristics at basilar membrane and inner hair cells; then, low-dimension sparse features are extracted by NTPCA for robust speaker modeling. The useful information of each subspace in the higher-order tensor can be preserved. Alternating projection algorithm is used to obtain a stable solution. Experimental results demonstrate that our method can increase the recognition accuracy specifically in noisy environments.