In this paper, mathematical model for cell growth and biofuel production under synthetic feedback loop is discussed. The nonlinear differential equations are solved analytically for the maximum production of biofuel under synthetic feedback. The closed-form of analytical expressions pertaining to the concentrations of cell density, repressor proteins, pump expressions, intracellular biofuel and extracellular biofuel are presented. The constant pump model is compared with feedback loop model analytically to know the biofuel production. The numerical solution of this problem is also reported using Scilab/Matlab program. Also, the analytical results are compared with previous published numerical results and found to be in good agreement.