Hyperspectral unmixing has been an important technique in remote sensing application. Sparse unmixing is a type of widely used methods, which assumes the endmembers in a hyperspectral image (HSI) are relatively small portion of the spectral library. The existing methods have considered single sparsity, row sparsity, and joint-sparsity-blocks regularizations to the unmixing model. However, they all reshape the HSI into a two-dimensional matrix, which results in the loss of local spatial information to some extent. So we consider the HSI as a tensor, and construct a new unmixing model based on the block term decomposition. Simultaneously, we propose a slice-sparsity-blocks regularization to fully utilize the local spatial information. In addition, tensor nuclear norm is added to the model to constrain the low rankness of the abundances, which can preserve the spatial structure and the interactions among the three dimensions. Then we design an efficient algorithm to solve the proposed model. And the experiments on the simulated dataset demonstrate the advantage of the proposed method.