This study aims at testing the weak form of efficient market hypothesis in the Nigerian capital market. The scope of the study consist of all securities traded on the floor of the Nigerian Stock Exchange and the month end value of the All Share Index from 2001 – 2010 constitute the data analyzed. The serial correlation technique of data analysis was used to test for independence of successive price movement and the distributive pattern while runs test was used to test for randomness of share price movement. The result of the serial correlation shows that the correlation coefficients did not violate the two-standard error test. Furthermore, the Box-Ljung statistic shows that none of the serial correlation coefficients was significant and the Box pierce Q statistics shows that the overall significance of the serial correlation test was poor while the result of the distribution pattern shows that stock price movements are approximately normal. on the basis of this findings ,we conclude that successive price changes of stocks traded on the floor of the Nigerian Capital Market are independent and random therefore, the Nigerian Capital Market is efficient in the weak-form.