Abstract: In the fields of pattern recognition, computer vision and image processing, data objects are typically represented as tensors. For dealing with tensor data, conventional methods usually convert them into feature vectors. However, this may results in the following problems: (1) break the inherent higher-order structure and correlation in the original data and lead to the loss of information; (2) generate the high dimensional feature vectors and thus make the subsequent learning process prone to overfitting, and suffer from the curse of dimensionality and the small sample size problems. In order to overcome these drawbacks, the studies on learning machines whose input patterns are tensors have recently attracted critical attention from the research community. Many tensor based classification algorithms have been proposed. At present, support higher-order tensor machine (SHTM) is one of the most effective algorithms for tensor classification. Considering that tensor objects are usually high dimensional and contain large amounts of redundancy, we propose a multilinear principle component analysis based support higher-order tensor machine (MPCA+SHTM) for tensor classification. In the proposed algorithm, multilinear principle component analysis is first used to conduct dimension reduction and preserve the natural structure and correlation in the original tensor data, then support higher-order tensor machine classifier is adopted for further redundancy elimination and classification. The experiments on twelve real tensor datasets show that MPCA+SHTM is faster than SHTM with comparable test accuracy