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Full-waveform inversion (FWI) is a powerful tool to reconstruct subsurface geophysical parameters with high resolution. As 3D surveys become widely implemented, corresponding 3D processing techniques are required to solve complex geological cases, while a large amount of computation is the most challenging problem. We propose an adaptive variable-grid 3D FWI on graphics processing unit devices to improve computational efficiency without losing accuracy. The irregular-grid discretization strategy is based on a dispersion relation, and the grid size adapts to depth, velocity, and frequency automatically. According to the transformed grid coordinates, we derive a modified acoustic wave equation and apply it to full wavefield simulation. The 3D variable-grid modeling is conducted on several 3D models to validate its feasibility, accuracy and efficiency. Then we apply the proposed modeling method to full-waveform inversion for source and residual wavefield propagation. It is demonstrated that the adaptive variable-grid FWI is capable of decreasing computing time and memory requirements. From the inversion results of the 3D SEG/EAGE overthrust model, our method retains inversion accuracy when recovering both thrust and channels.