Grid has been widely used in the field of evolutionary multi-objective optimization (EMO) due to its property combining convergence and diversity naturally. Most EMO algorithms of grid-based fitness perform well on problems with two or three objectives, but encounter difficulties in their scalability to many-objective optimization. This paper develops the potential of using grid technique to balance convergence and diversity in fitness for many-objective optimization problems. To strengthen selection pressure and refine comparison level, three hierarchical grid-based criterions are incorporated into fitness to establish a completer order among individuals. Moreover, an adaptive fitness penalty mechanism in environmental selection is employed to guarantee the diversity of archive memory. Based on an extensive comparative study with three other EMO algorithms, the proposed algorithm is found to be remarkably successful in finding well-converged and well-distributed solution set.