For a multi-fingered hand to grasp an object, there are numerous ways to grasp it stably, and thus an optimal grasp planning is necessary to find the optimal grasp point for achieving the objective of the given task. First, we define several grasp indices to evaluate the quality of each feasible grasp. Since the physical meanings of the defined grasp induces are different from each other, it is not easy to combine those indices to identify the optimal grasping. In this paper, we propose a new generalized grasping performance index to represent all of the grasp indices as one measure based on a non-dimensional technique. Through simulations, we show that the proposed optimal grasp planning is resemblant to the physical sense of human grasping.