The high level of unemployment and poor power supply to the industrial sector are the major problems facing the Nigerian economy. For the past two decades, successive governments in Nigeria have made futile attempts to address the issues of unemployment. Several scholarly studies have been conducted to establish relationships between unemployment and microeconomic variables without any serious attention on the relationship between unemployment and electricity power supply. The study addresses the question of the impact of electricity power on unemployment rates in Nigeria. This study using an ordinary least square regression model examined the influence of electricity power outputs, supply and consumption in addressing the high rate of unemployment in Nigeria. The study which covers the period of 1970 to 2005 discovers that power supply to the industrial sector was lower than the supply for residential consumption. The study also establishes that the major cause of unemployment in Nigeria can be traced to inadequate and unstable power supply to the industrial sector. The study advises the government and the policy makers to invest more in electricity power generation and ensures that the industrial sector is given a higher priority in the supply of electricity if the high unemployment rate is to be abated.