This study examines the random walk hypothesis on security returns in the Nigeria. The primary  objective was to test random walk hypothesis on security returns in the Nigeria capital  market.This study made use of annual data collected from the Nigerian stock exchange (NSE)  between 1986- 2017. However, in order to validate the random walk theory in the Nigeria  bourse, unit root test was adopted and the hypothesis was tested at a critical value of 5% and  10% respectively. The findings from the analysis reveal that the Nigeria capital market is  currently nonrandom. This implies that and participant can outperform the market with past  return if they can efficiently allocate their asset. We therefore recommended that investors  should put into consideration the trend of movement of returns in other to maximize their  portfolio.