In this paper we develop a Jacobi-type algorithm for the (approximate) diagonalization of tensors of order d ≥ 3 via tensor trace maximization. For a general tensor this is an alternating least squares algorithm and the rotation matrices are chosen in each mode one-by-one to maximize the tensor trace. On the other hand, for symmetric tensors we discuss a structurepreserving variant of this algorithm where in each iteration the same rotation is applied in all modes. We show that both versions of the algorithm converge to the stationary points of the corresponding objective functions.