Droop control are widely adopted in DC microgrids to achieve equal current sharing of distributed battery systems (DBS). However, as equivalent resistances of cables and circuit components between the DBS and the microgrid will change over the long-term operation of the system, unequal current sharing of the DBS that use conventional droop control with constant virtual resistances may accelerate the uneven ageing of the battery packs. To resolve this issue, in this paper, an adaptive virtual resistance-based droop control, which adapts to the change of the equivalent resistances to achieve adaptive current sharing of DBS, is proposed. With this method, the output currents of DBS are fed to a central controller via a communication network and is then controlled by proportional-integral (PI) controllers to generate a set of variable virtual resistances. These parameters are then added to the original static virtual resistances of the droop control to form the adaptive virtual resistances. Furthermore, to ensure precise current sharing of DBS, a Differential Evolution (DE) algorithm is introduced to optimize the parameter tuning of the PI controllers. Both simulation and experimental results validate the current sharing capabilities of DBS under the proposed control in handling the change of equivalent resistances. Besides, the results also demonstrate that the DBS controlled by the proposed control with sub-optimal tunings of the PI controllers can result in slight unequal current sharing.