Unlike conventional haptic devices, an encountered-type device is not held by a user all the time. Instead, the device stays at the location of a virtual object and waits for the user to encounter it. In this paper, we extend this concept to fingertip contacts and design an encountered-type haptic display for multiple fingertip contacts to simulate tasks of grasping an object with any shape and size. Before designing the device, we intensively observed human grasping behaviors. This observation was very helpful to determine the mechanism of the device. An encountered-type device for three-fingered grasping was actually prototyped based on our design.