A voltage regulator (VR) for a processor is one of the most critical platform components. Particularly, a VR is required to support fast, accurate, and fine-grained voltage changes for efficient processor power management. Such requirements, nonetheless, can be relaxed when a processor consumes low power at runtime. Thus, manufacturers begin to offer some knobs so that a processor can adapt VR's operating parameters to cost-effectively satisfy the requirements with high efficiency. In this paper, we first demonstrate that: (1) VR efficiency heavily depends on load current (i.e., current delivered to a processor) and a VR operating parameter (e.g., the number of active phases) at given voltage; (2) a processor running a parallel application mostly consumes small current due to aggressive power management; and (3) when the processor is in active state, all the phases are always activated in the VR. (2) and (3) in turn lead to poor VR efficiency at most runtime. Second, we present VR-Scale that dynamically scales the number of active phases based on the predicted load current for the next interval. Our evaluations based on an Intel processor running emerging parallel applications show that VR-Scale can reduce the total power consumed by a processor and its VR by more than 19% with negligible performance impact.