Forecasting a financial time series, such as stock market trends, would be a very important step when developing investment portfolios. This step is very challenging due to complexity and presence of a multitude of factors that may affect the value of certain securities. In this research paper, we have proved by contradiction that the Nigerian stock market is not efficient but chaotic. Two years representative stock prices of some banks stocks were analyzed using a feed forward neural network with back-propagation in Matlab 7.0. The simulation results and price forecasts show that it is possible to consistently earn good returns on investment on the Nigerian stock market using private information from an artificial neural network indicator.