Recent development in data-driven decision science has seen great advances in individualized decision making. Given data with individual covariates, treatment assignments and outcomes, policy makers search for the best individualized treatment rule (ITR) that maximizes the expected outcome, known as the value function. In this paper, we consider the problem of finding an ITR from a restricted ITR class where there is some unknown covariate changes between the training and testing distributions. We propose a novel distributionally robust ITR (DR-ITR) framework that maximizes the worst-case value function across the values under a set of underlying distributions that are "close" to the training distribution. The resulting DR-ITR can guarantee the performance among all such distributions reasonably well. We further propose a calibrating procedure that tunes the DR-ITR adaptively to a small amount of calibration data from a target population. In this way, the calibrated DR-ITR can be shown to enjoy better generalizability than the standard ITR based on our numerical studies.