Reconstructing 3D parameter maps of huge volumes entirely on the GPU is highly desirable due to the offered computation speed-up. However, GPU memory restrictions limit the coverable volume. To overcome this limitation, a double-buffering strategy in combination with model-based parameter quantification and 3D-TGV regularization is proposed. This combination warrants whole volume reconstruction while maintaining the speed advantages of GPU-based computation. In contrast to sequential transfers, double-buffering splits the volume into blocks and overlaps memory transfer and kernel execution concurrently, hiding memory latency. The proposed method is able to reconstruct arbitrary large volumes within 5.3 min/slice, even on a single GPU.