This paper presents a new method to determine voltage stability index value in a three phase radial distribution system. The proposed method is a new application of extreme learning machine combined with the positive sequence catastrophe theory voltage stability index method (P.S Cat Theory VSI). Catastrophe theory method is the latest method to calculate VSI values in one phase radial distribution system. Then, this method is developed by adding the positive sequence concept into the calculation. This addition makes sure that catastrophe theory can be applied for three phase radial distribution system. The calculation results are used as data output in extreme learning machine, while the input is positive sequence voltage value of each bus. Neural network (NN) is used in the simulation to compare the computation speed and performance between NN and the proposed method. The result shows that computation speed and performance of the proposed method is better than neural network method.