The incessant power outages that characterize the Nigerian power network (NGP), as in all developing countries, are not limited to the shortage of fuel for power generation. However, differential power shortages between the generated power and the load demand are alarming. In this study, we propose a new voltage stability pointer (NVSP) based on a reduced one-line power network to act as a classifier. The NVSP was trained with a support vector machine (SVM) using a medium Gaussian kernel classification toolbox (mGkCT) in the MATLAB environment. This classification is based on the power network susceptibility to voltage instability. NGP 28-bus 330 kV data were extracted and modeled in the MATLAB environment and tested with the NVSP-mGkCT classifier. The NVSP-mGkCT was able to classify the lines viz. stable and unstable lines for the base and contingency cases. Similarly, the linear load dynamics and non-linear load dynamics were evaluated on the basis of critical buses using the NVSP. The aim of this work was to help the Transmission Company of Nigeria (TCN) and the National Control Centre (NCC) to be pre-emptive with respect to possible voltage collapse due to voltage instability. The simulation results show that NVSP was able to flag vulnerable lines in the NGP.