Biodiesel has emerged as one of the alternative biofuels to non-renewable fuels, and the typical method of producing biodiesel is by transesterification process. This process was employed in the present work to synthesize biodiesel from waste vegetable oil using acid and base catalysis methods to improve the yields and to identify the optimum operating conditions. Response surface methodology was used to determine the optimum operating parameters. The free fatty acids (FFAs) in the oil were reduced using acid catalyst (H2SO4) before a base catalyst (NaOH) was added. The duration for acid catalyzed process was determined such that it was just short enough to esterify the FFAs that were in the oil. The subsequent base catalyzed synthesis results showed that biodiesel was formed and the highest biodiesel yield was at 2% weight catalyst, 50°C and reaction time of 1.5 h. A further increase in temperature at 2% catalyst weight favoured the formation of soap and had a negative impact on the yield of biodiesel. The yield increased with an increase in temperature, catalyst weight and reaction time. The highest yield was at 3% weight catalyst, 60°C and reaction time of 2 h. The results of the acid-base catalyzed synthesis showed that biodiesel yield was improved as compared to the base catalyzed synthesis alone due to the fact that acid catalyst was responsible for esterifying the FFAs, and subsequently when the base catalyst was added, more biodiesel was formed because no soap formation took place in the reaction. The kinematic viscosity of acid-base catalyzed biodiesel satisfied the standard test method for kinematic viscosity (ASTM D445).