Joint diagonalization (JD) of high-order tensors is a generalization of an approximate JD algorithm of a series of target matrices. Considering the number of target tensors may increase with time, we present an adaptive nonunitary JD algorithm of high-order tensors. The algorithm recursively minimizes a least squares criterion and updates diagonalizer matrices by the online algorithm and tensor calculations. The complexity of our algorithm is lower than the iterative algorithms. Simulation results demonstrate that the proposed algorithm is efficient for JD of high-order tensors.