This talk discuss the tensor maximal correlation problem, which aims at optimizing correlations between sets of variables in many statistical applications. We reformulate the problem as an equivalent polynomial optimization problem, by adding the fifirst order optimality condition to the constraints, then construct a hierarchy of semidefifinite relaxations for
solving it. The global maximizers of the problem can be detected by solving a fifinite number of such semidefifinite relaxations. Numerical experiments show the effificiency of the proposed method.