Extensive consumption of fossil fuel has contributed to the worldwide decline of its reserves and detrimental effect on the environment. Therefore, it is essential to explore alternative option of fuel for diesel engine. The main objective of this research article is to optimize vibrations in a single-cylinder variable compression ratio diesel engine driven by Jatropha biodiesel blend. The heterogeneous catalyst (calcium oxide) is used to manufacture of biodiesel from Jatropha curcas oil by a process of transesterification. The optimization technique (Response Surface Methodology) has been employed to optimize root mean square acceleration of vibration by taking load, compression ratio (CR), and fuel injection pressure (FIP) as engine input parameters. Experiments were designed according to central composite design. The amplitude of the frequency domain signals is determined using Fast Fourier Transform and the influence of input parameters has been investigated in the frequency domain analysis of the vibration signatures. The adequacy and significance of the models have been checked by p-value and F value tests. Regression coefficients Adj. R2, R2, Pred. R2 were also found in acceptable range. The experimental outcome reveals that biodiesel yield of 81.6% was obtained at methanol-to-oil molar ratio of 12:1, reaction temperature of 65°C, reaction time of 3 h, and catalyst concentration of 5 wt%. Simultaneously, the model obtained a series of solutions based on the desirability criteria and proposed optimum setting of engine input parameters at a load of 2.59 kg, 17.94 CR, and 268.76 bar FIP for B30 blend. B30 blend generated root mean square acceleration of 4.46 m/s2 at above optimized conditions. A validation trial was conducted and the percentage of error for root mean square acceleration was found to be 2.3356% and 1.3039%, respectively, for B0 and B30 blend.