In this study, a mathematical model for the trans-esterification reaction of Jatropha curcas seed Oil (JCO) was developed using Response Surface Methodology (RSM) in terms of some operational variables, namely: temperature (50 to 80°C), catalyst concentration (0.7 to 1% in relation to oil mass) and methanol/oil ratio (3:1-9:1), at fixed reaction time (90 min) and mixing intensity. Biodiesel was produced by trans-esterification of J. curcas seed oil with methanol using NaOH as catalyst. Optimum biodiesel yield of 88.64% was obtained at 7:1 molar ratio of methanol/oil, reaction temperature of 80°C and 0.8% catalyst loading. The biodiesel produced at 80°C, 7:1 methanol/oil ratio and 0.9% catalyst loading when blended with petro-diesel (B20) gave the highest Cetane number of 81.83. The results obtained indicated that the reaction temperature, methanol/oil ratio and catalyst concentration have significant effects on both the Cetane number and yield of biodiesel. Thus, the mathematical model developed can be used in the optimization and simulation of biodiesel yield during trans-esterification of vegetable oil within the range of the parameters studied.