Sub-tensor based lower rank tensor analysis used for dimensionality reduction and classification in hyperspectral imagery is proposed in this paper. The method aims at raising classification accuracy by representing the hyperspectral image as a tensor, divides it into sub-tensors and performs dimensionality reduction and pixel classification in each sub-tensor. Owing to the idea of creating sub-tensors, the method capitalizes on local spatial correlation, exploits interaction between spatial and spectral dimensions, and maintains hyperspectral data structure with 3D tensor. Compared with existing theories based on tensor analysis, the proposed method eliminates the negative impacts of poor subspace dimension estimation and low global spatial correlation, which might seriously degrade performances of dimensionality reduction. Moreover, as long as subspace dimensions are smaller than sub-tensor dimensions, the method with sub-tensors achieves much higher classification accuracy than the method without sub-tensors. Therefore, for the proposed method, it is not necessary to estimate the subspace dimension. Finally, experimental results of both simulated and real hyperspectral data demonstrate that Sub-Tensor based Lower Rank Tensor Analysis gives better performance in dimensionality reduction and brings higher classification accuracy than existing methods do.