Hierarchical sensitivity analysis of multilevel systems is to assess the effect of system's input uncertainties on the variations of system's performance through integrating the sensitivity indices of subsystems. However, it is difficult to deal with the engineering systems with complicated correlations among various variables across levels by using the existing hierarchical sensitivity analysis method based on variance decomposition. To overcome this limitation, a mapping-based hierarchical sensitivity analysis method is proposed to obtain sensitivity indices of multilevel systems with multidimensional correlation. For subsystems with dependent variables, a mapping-based sensitivity analysis, consisting of vine copula theory, Rosenblatt transformation and polynomial chaos expansion technique, is provided for obtaining the marginal sensitivity indices. The marginal sensitivity indices can allow us to distinguish between the mutual depend contribution and the independent contribution of an input to the response variance. Then extended aggregation formulations for local variables and shared variables are developed to integrate the sensitivity indices of subsystems at each level so as to estimate the global effect of inputs on the response. Finally, this paper presents a computational framework that combines related techniques step by step. The effectiveness of the proposed mapping-based hierarchical sensitivity analysis method is verified by a mathematical example and a multiscale composite material.