Skyline computation is an essential database operation that has many applications in multi-criteria decision making scenarios such as recommender systems. Existing algorithms have focused on checking point domination, which lack efficiency over large datasets. We propose a grid-based structure that enables grid cell domination checks. We show that only a small constant number of cells need to be checked which is independent from the number of data points. Our structure also enables parallel processing. We thus obtain a highly efficient parallel skyline algorithm named SkyCell, taking advantage of the parallelization power of graphics processing units. Experimental results confirm the effectiveness and efficiency of SkyCell -- it outperforms state-of-the-art algorithms consistently and by up to over two orders of magnitude in the computation time.