A motion planning algorithm is proposed for an encountered-type haptic device that can simulate grasping tasks by multiple fingertips. The algorithm determines the location of each surface patch of the device from the weighted mean of the all minimum distance point information on the virtual objects from each fingertip of the user. By carefully designing the weights, the proposed algorithm can work for not only convex objects but also concave ones. The proposed pathplanning algorithm is also designed to avoid any collision with the user in transition phases between subsequent contacts by introducing a prohibited area around the user?s hand. The effectiveness of the proposed algorithm is confirmed by simulations.