Optimization of biodiesel production from non-edible papaya seed oil was investigated in this study. Biodiesel production process parameters such as catalyst concentration, methanol:oil molar ratio and reaction temperature were optimized by using the Response Surface methodology based on the Box-Behnken experimental design. Optimization of the transesterification process was conducted by varying three factors each at three different levels and this required a total of fifteen runs. A quadratic model was created to predict the biodiesel yield where the R-2 value was found to be 0.99 which indicates the satisfactory accuracy of the model. Based on the results, the optimum process parameters for transesterification of the papaya seed oil mixture at an agitation speed of 600 rpm over a period of 60 min were found to be a methanol:oil molar ratio 10:1, KOH catalyst concentration of 1 wt% and reaction temperature of 45 degrees C. At these reaction conditions, the predicted and experimental biodiesel yield were 96.12% and 96.48% respectively which shows less than 0.5% variation. The biodiesel properties were characterized and the results obtained were found to satisfy both ASTM D6751 and EN14214 standards. The statistical tool MINITAB 17 was used to draw both 3D surface plots and 2D contour plots to predict the optimum biodiesel yield.