The efficient digital image processing technology is widely used in the fields of big data and artificial intelligence, especially hyperspectral image processing, which has become a hot topic in academic research. Hyperspectral data are usually stored in the form of high-dimensional arrays. However, the matrixization method of high-dimensional arrays lacks generalization ability as its internal structure cannot be accurately interpreted. In this paper, a novel tensor completion algorithm is proposed to reconstruct hyperspectral image and analyze the corresponding data. Firstly, a tensor kernel norm optimization model with regularization is established for hyperspectral image processing. Secondly, a new multi-multiplier algorithm with variable parameter alternating-direction is proposed to solve the tensor optimization model, and the convergence theory is established. Finally, the feasibility and effectiveness of the algorithm are verified by multi-dimensional comparison and analysis with some current effective algorithms.