In order to realize the observation of voltage sag at any position in power system, an optimal allocation method of voltage sag monitoring nodes based on the minimum magnitude search is proposed. Firstly, according to the analytic formula of voltage sag, the minimum node voltage magnitude when the fault location changes in each line is searched by golden section method. Based on the voltage threshold, the monitor reach area and the worst observable matrix are constructed under different fault types. Finally, with the constraint of fully observable voltage sag at any position, the optimal allocation model is established to minimize the voltage sag monitoring nodes. When constructing the voltage sag observable matrix, the worst scenario of voltage sag is considered to avoid monitoring blind area. The accuracy and effectiveness of proposed method are verified based on IEEE 30-bus system.