In this paper, a vertically moving base inverted pendulum control analysis has been done using Matlab/Simulink Toolbox. Because the vertically moving base inverted pendulum system is nonlinear and highly unstable, a feedback control system is used to make the system controlled and stable. A nonlinear autoregressive moving average L2 controller which is a family of Neural Network controller is used with Resilient backpropagation and Levenberg Marquardt backpropagation Training Algorithm to improve the stability of the pendulum. Comparison of the vertically moving base inverted pendulum using NARMA-L2 with Resilient backpropagation and Levenberg Marquardt backpropagation Training Algorithm for tracking a desired angular position of the system using a step and random input signals and a promising results have been obtained succesfully.