A continuous power flow (CPF) calculation method for the islanded microgrids with droop control is proposed in this paper. The starting point of CPF is solved by the modified factored load flow algorithm. The algorithm ensures the robustness of the starting point calculation with a two-step solution. The tangent prediction method and the Newton-Raphson method are used to determine the prediction and correction steps. Further, this paper proposes an adaptive step size control method based on frequency variation, which avoids the comparison among different nodal voltage magnitudes. In addition, node type switching is considered for handling the limit violations of PV nodes and droop nodes. The case analysis shows that the proposed CPF method has high efficiency and strong robustness.