Tensor decomposition (TD) is widely used in hyperspectral image (HSI) compression. we note that the correlation in HSI may be helpful to improve the HSI compression performance of TD methods. The initialization of factor matrix in TD can determine the HSI compression performance. Meanwhile, it is worth noting that HSI is highly correlated in bands. In this paper, we propose a method called correlation-based TD initialization algorithm. By analyzing the optimization of TD, we find that the initialization of TD can be well approximated by a matrix decomposition. Thus, we adopt the mean band of HSI to approximate the initialization of TD. In accordance with the SVD result of the reference band, the initialized factor matrices of TD are produced. We compare our methods with other compression methods. The experimental results reveal that our correlation-based TD initialization method is capable of significantly reducing the computational cost of TD while keeping the initialization quality and compression performance.