The AutoDock suite is widely used molecular docking software consisting of two main programs -- AutoGrid for precomputation of potential grid maps and AutoDock for docking into potential grid maps. In this paper, the acceleration of potential maps generation based on AutoGrid and its implementation called FastGrid is presented. The most computationally expensive algorithms are accelerated using GPU, the rest of algorithms run on CPU with asymptotically lower time complexity that has been obtained using more sophisticated data structures than in the original AutoGrid code. Moreover, the CPU implementation is parallelized to fully exploit computational power of machines that are equipped with more CPU cores than GPUs. Our implementation outperforms original AutoGrid more than 400x for large, but quite common molecules and sufficiently large grids.