The contributions of error distributions have been ignored while modeling stock market volatility in Nigeria and studies have shown that the application of appropriate error distribution in volatility model enhances efficiency of the model. Using Nigeria All Share Index from January 2, 2008 to February 11, 2013, this study estimates first order symmetric and asymmetric volatility models each in Normal, Student's-t and generalized error distributions with the view to selecting the best forecasting volatility model with the most appropriate error distribution. The results suggest the presence of leverage effect meaning that volatility responds more to bad news than it does to equal magnitude of good news. The news impact curves validate this result. The last twenty eight days out-of-sample forecast adjudged Power-GARCH (1, 1, 1) in student's t error distribution as the best predictive model based on Root Mean Square Error and Theil Inequality Coefficient. The study therefore recommends that empirical works should consider alternative error distributions with a view to achieving a robust volatility forecasting model that could guarantee a sound policy decisions.