Recently, there are several multilinear methods have been proposed for tensorial data dimensionality reduction (feature extraction). However, there are few new algorithms for tensorial signals classification. To solve this problem, in this paper, a novel classifier as a tensor extension of extreme learning machine for multi-dimensional data recognition is introduced. Due to the proposed solution can classify tensorial data directly without vectorizing them, the intrinsic structure information of the input data can be reserved. Moreover, compared with the traditional ELM, much fewer parameters need to be calculated through the proposed tensor based classifier. Extensive experiments are carried out on different databases, and the experiment results are compared against state-of-theart techniques. It is demonstrated that the new tensor based classifier can get better recognition performance with an extremely fast learning speed.