Wrapping-based informed RRT∗ is a modified version of informed RRT∗. Informed RRT∗ formulates an n-dimensional hyperellipsoid from which it generates new sample nodes. This has a dramatically increased chance of sampling nodes that will improve the current best solution compared to conventional RRT∗. However, due to explorative and randomized behaviors of RRT∗, the size of the hyperellipsoid will unlikely be small enough to call it effective. To solve this matter, wrapping-based informed RRT∗ proposed in this paper combines a size-diminishing procedure called 'wrapping process' with informed RRT∗. The proposed planner can advance from the first solution acquired by the planner to the improved, feasible solution which can drastically reduce the size of the hyperellipsoid. Therefore, the required time consumption in order to acquire the globally optimal solution is reduced dramatically. The algorithm was tested in various environments with different numbers of joint variables and showed much better performance than the existing planners. Furthermore, the wrapping process proved to be a comparably insignificant computational burden regardless of the number of dimensions of the configuration space.