This paper applies the truncated singular value decomposition method (TSVD) with adaptive pruning L-curve technique to solve numerically the two dimensional ill- posed inverse problem of gravity anomalies. The inverse problem here is to determine a plausible spatial variation of density within the earth that is consistent with a finite set of geophysical observations. To reduce the ambiguity; the problem was solved as an overdetermined one and linear constraints were added. The results obtained are compared to exact solutions of simple and complicated synthetic earth models with and without noise. It is found that TSVD with adaptive pruning L-curve technique is stable, robust and it always converges to the right solutions. Furthermore, the method is successfully applied to a real data example from USA.