A contemporary and decisive optimization algorithm is developed for inverting gravity anomalies due to listric faults. The cross-section of listric faults are generally concave up, and the dip of the fault plane gradually decreases with depth. Quadratic Bezier curves are utilized to represent the curvature of the fault plane. The densities of sediment deposition are assumed to be known and can take any functional form of depth. By constraining the density, a global optimization algorithm is adopted to estimate the fault structure by inverting control point parameters of Bezier curves. The presented algorithm is implemented in two different synthetic models having fixed and depth varying density contrasts. The robustness of the algorithm is authenticated by incorporating white Gaussian noise into synthetic gravity anomalies. A detailed uncertainty appraisal is also performed to justify the reliability of the algorithm. Finally, a real structure is reconstructed using observed gravity anomalies, and the estimated structure is verified with the structure obtained in previously published literature. Furthermore, a Matlab based GUI is developed such that any user can estimate real listric fault structure without any computational difficulties.