Abstarct: Gravity data inversion is one of the most important steps in the interpretation of these data. The aim is to estimate the unknown model subsurface density distribution through the data measured at the earth's surface. The main problem in the inversion of the gravity data, geophysical data inversion is caused by lack of uniqueness of solutions. Linear inversion gravity data problem is determined low and ill posed. Determine the optimal regularization parameter inversion of gravity data is of great importance. One of these methods, is the method of generalized cross validation (GCV). In this thesis quadratic programming method (quadratic method), an optimization method is used. This method has three algorithms, is the trust region, the interior point and active set. The three inversion algorithms duration of implementation as well as the stability of each of these algorithms will be reviewed for noise. In order to validate the proposed method, the gravity data derived from synthetic and were used gravity data mobrun sulfide copper mine located in Quebec, Canada.