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Gravity anomaly inversion is a technique used to estimate underground density distribution using gravity data. This paper proposes a new three-dimensional (3D) gravity anomaly inversion method based on the LinkNet network. Compared with two-dimensional gravity anomaly inversion, 3D gravity anomaly inversion can determine the density distribution of the entire region below the observation surface. Additionally, compared with traditional methods, the neural network method does not require the selection of initial parameters, and several predictive models can be quickly sought during the prediction stage. The Tversky loss was used to improve the inversion accuracy of the boundary. By comparing the inversion of the fully convolutional network, UNet network, and LinkNet network proposed in this paper on simulated data, it was observed that the model reconstruction error obtained using the LinkNet network had the best fitting effect with gravity data, which were 0.3526 and 0.0521. The results reveal that this method can achieve accurate inversion. Using the San Nicolas deposit in Mexico as an example, the proposed method and the improved preconditioned conjugate gradient algorithm were compared to further illustrate the effectiveness of the algorithm. The results reveal that the position and shape trends of the geological body attained using the proposed approach are in good agreement with the drilling data. [ABSTRACT FROM AUTHOR]