The Rapidly-exploring Random Tree (RRT) algorithm is a popular algorithm in motion planning problems. The optimal RRT (RRT*) is an extended algorithm of RRT, which provides asymptotic optimality. This paper proposes Quick-RRT* (Q-RRT*), a modified RRT* algorithm that generates a better initial solution and converges to the optimal faster than RRT*. Q-RRT* enlarges the set of possible parent vertices by considering not only a set of vertices contained in a hypersphere, as in RRT*, but also their ancestry up to a user-defined parameter, thus, resulting in paths with less cost than those of RRT*. It also applies a similar technique to the rewiring procedure resulting in acceleration of the tendency that near vertices share common parents. Since the algorithm proposed in this paper is a tree extending algorithm, it can be combined with other sampling strategies and graph-pruning algorithms. The effectiveness of Q-RRT* is demonstrated by comparing the algorithm with existing algorithms through numerical simulations. It is also verified that the performance can be further enhanced when combined with other sampling strategies. (C) 2019 Elsevier Ltd. All rights reserved.