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Inversion of the gravity gradient data is widely adopted to construct 3-D density models. However, this inversion usually suffers from non-uniqueness and has a limited resolution in depth. This study introduces an effective inversion method for interpreting gravity gradient data based on the mixed L1 and L2 norm regularization. We also apply an efficient forward modeling algorithm to the inversion, which has many time-consuming iterations. Equivalence relations in the sensitivity matrix are employed to reduce the storage and computation time. In addition, a 2-D discrete convolution algorithm is used to reduce the repetitive calculation in the forward modeling. The numerical examples demonstrate that the computational efficiency is increased by about three orders of magnitude compared with the traditional forward method. Furthermore, compared to traditional single-norm inversion, the vertical gradient inversion with the mixed L1 and L2 norm regularization has a higher depth resolution. Finally, we apply the method to the inversion of the airborne gravity gradiometry data over the Vinton Dome, southern Louisiana.