A twisted-fin array as an innovative structure for intensifying the charging response of a phase-change material (PCM) within a shell-and-tube storage system is introduced in this work. A three-dimensional model describing the thermal management with charging phase change process in PCM was developed and numerically analyzed by the enthalpy-porosity method using commercial CFD software. Efficacy of the proposed structure of fins for performing better heat communication between the active heating surface and the adjacent layers of PCM was verified via comparing with conventional longitudinal fins within the same design limitations of fin material and volume usage. Optimization of the fin geometric parameters including the pitch, number, thickness, and the height of the twisted fins for superior performance of the proposed fin structure, was also introduced via the Taguchi method. The results show that a faster charging rate, higher storage rate, and better uniformity in temperature distribution could be achieved in the PCMs with Twisted fins. Based on the design of twisted fins, it was found that the energy charging time could be reduced by up to 42%, and the energy storage rate could be enhanced up to 63% compared to the reference case of straight longitudinal fins within the same PCM mass limitations.