Waste cooking oil (WCO) is converted into methyl ester using transesterification. Various mixtures of biodiesel and diesel oil in ratios of 25, 50, 75, and 100% were created and approved by ASTM. Several experiments are conducted to investigate engine performance and emissions of biodiesel blends. Two mathematical models as extreme learning machine (ELM) and quadratic regression are developed to predict engine parameters and emissions at different engine speeds and biodiesel concentrations. At peak output power and engine speed of 1500 rpm, the lowest output power of the 100% methyl ester mixture is 25% lower than crude diesel. Largest increases of exhaust gas temperature and specific fuel consumption about diesel oil for biodiesel were 28 and 23 %, respectively. Biodiesel has equivalence ratio and volumetric efficiency as 15% and 4% lower than diesel. At 1500 rpm engine speed, the 100% biodiesel blend reduces CO, CO2, HC, and smoke concentrations by 12, 13, 44 and 48% respectively about diesel oil, while resulting in 23% more NOx emission. Quadratic regression is favorable about ELM in predicting engine performance and emissions for most variables achieving lower rootmean square and mean absolute percentage errors. Biodiesel from WCO is a promising substitute fuel in diesel engines.