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This paper presents a new fast method to detect the long term voltage instability of power system based on wide area measurement system (WAMS). The objective of this paper is to quickly assess the long term voltage instability, which may be occurred by load disturbance, using the measurements gathered from phasor measurement units (PMUs). The main features of this method is the preprocessing of the measured data using the mathematical morphology method, and classification of the chosen features using the support vector machine (SVM) to assess the voltage stability of power system. The simulation results have shown that the proposed method can effectively determine the voltage instability of power system at a very short time after the load disturbance.