Tensor decomposition (TD) is widely used in hyperspectral image (HSI) compression. The initialization of factor matrix in tensor decomposition can determine the HSI compression performance. It is worth noting that HSI is highly correlated in bands. However, this phenomenon is ignored by the previous TD method. Aiming at improving the HSI compression performance, we propose a method called correlation-based TD initialization algorithm. As HSI is well approximated by means of a reference band. In accordance with the SVD result of the reference band, the initialized factor matrices of TD are produced. We compare our methods with random and SVD-based initialization 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.