Vulnerability assessment in power systems is important so as to determine how vulnerable a power system in case of any unforeseen catastrophic events. This paper presents the application of Radial Basis Function Neural Network (RBFNN) for vulnerability assessment of power system incorporating a new proposed feature extraction method named as the Neural Network Weight Extraction (NNWE) for dimensionality reduction of input data. The performance of the RBFNN is compared with the Multi Layer Perceptron Neural Network (MLPNN) so as to evaluate the effectiveness of the RBFNN in assessing the vulnerability of a power system based on the indices, power system loss and possible loss of load. In this study, vulnerability analysis simulations were carried out on the IEEE 300 bus test system using the Power System Analysis Toolbox and the development of neural network models were implemented in MATLAB version 7. Test results prove that the RBFNN give better vulnerability assessment performance than the multilayer perceptron neural network in terms of accuracy and training time. The proposed feature extraction method decreases the training time drastically from hours to less than seconds, this bound to influence the vulnerability classification and increase the speed of convergence. It is also concluded that the reduction in error is achieved by using PSL as an output variable of ANN, in all the cases the error of RBFNN output by PSL is less than 4.87% which is well within tolerable limits.