The computational efficiency of the forward modeling for gravity and gravity gradient anomalies determines the feasibility of inverse modeling. It also forms the basis for the efficient building of sufficient and diverse deep learning sample data. Inspired by the application of moving-footprint—a fast forward modeling method in the aerospace electromagnetic field and based on the fast space-domain forward modeling of geometric lattice functions of grid points, the authors proposed a computation method for the forward modeling of gravity and gravity gradient anomalies by applying “moving-footprint”, aiming to further improve the speed of the forward calculation for gravity and gravity gradient anomalies. Specifically, this method selects the subspace in a certain effective range directly below an observation point in the underground half-space. The observation point anomaly approximates the total anomalies of the cuboid units in the corresponding subspace while ignoring the anomalies produced by the cuboid units outside the subspace. When the observation point moves, the corresponding subspace moves accordingly. Therefore, the large-scale underground half-space cuboid model can be decomposed into the subspace corresponding to each calculation point for the forward calculation. As shown by the results of a model test, when 32×32×15 subspace was selected in the underground half-space of a 256×256×15 rectangular parallelepiped model for calculation, the relative average error of gravity anomalies and partial gradient anomalies was less than 10% and the calculation speed was increased by 19 times. Moreover, the calculation time of 1024×1024×15 rectangular parallelepiped model is approximately 32 minutes. Compared with the existing algorithms with a bottleneck in the ultra-conventional calculations, the method proposed in this study has significant advantages regarding computation.