The main objective of this study was production, optimization, and fuel quality characterization of biodiesel from equal weight ratio blended acid oil of cottonseed and sunflower soapstock using silica sulfuric acid as a solid acid catalyst in laboratory scale. The physicochemical properties of soap stock samples and extracted acid oil from each soap stock were determined. The experiment was designed by design expert (version 11) software. The 5-level 4-factors (methanol to acid oil molar ratio, catalyst weight, stirring rate, and reaction time) were designed using the central composite design method. From the experimental results, the maximum biodiesel yield of 90.68% was obtained using methanol to acid oil molar ratio of 7:1 using catalyst 5.5(%wt/wt) with a stirring rate of 300rpm at 3hr reaction time. The average value of triplicate experiment of biodiesel yield from the experimentation at optimized condition was 92.62%. The analysis of variance results indicated that satisfactory results were achieved. The carried out physiochemical properties of produced biodiesel were within a range and some were closest to American and European biodiesel standards.