Smooth-switching of microgrid to islanded mode is of the important to guarantee the continuous power supply to the important loads. This paper firstly studies the V/f controller of the microgrid that operates in islanded mode， and establishes a small-signal state space model for inverter based on the V/f controller. Then the eigenvalues are used to analyze the stability in the smooth-switching when the V/f controller parameters， the load impedance and the equivalent line impedance change. The results are verified by time-domain simulations. Secondly， the sensitivity of the parameters to the dominant eigenvalues is analyzed when the power load level changes. Finally， the dominant parameters and factors that can guarantee the microgrid to achieve smooth-switching are obtained， which can be the reference for the switching control methods and strategies.