This letter proposes a virtual slack bus Newton-Raphson power flow (VSB-NRPF) algorithm serving for the PF analysis of droop-controlled medium-voltage direct current (MVDC) systems operating in islanded mode without a slack bus. In the proposed algorithm, one of the original power, current, power/voltage and current/voltage buses is assumed to be a virtual slack bus with an initial rated dc voltage, the value of which is corrected based on the actual PF balance equation at the original bus.