Stable grasping for soft food objects, such as tofu, by a conventional gripper without any damages is very difficult, because such objects have an indeterminate form and are extremely fragile. For soft and fragile objects grasping, this paper proposes a passively deformable soft finger that utilizes an internal air pressure control system with an air pump. The finger has a soft bag component that has air inside. The soft bag deforms its shape according to the shape of the object being held. The internal air pressure is controlled when the finger is holding an object so as to keep the air pressure at a constant value. This leads to a wrapping grip that can increase the contact area with the object, which lowers the contact pressure on the object. In this paper, the design of the fingertip and the validation for the fragile object grasping are shown at the beginning, then the contact force and the contact pressure distribution applied by the fingertip are experimentally investigated in order to estimate the gripping force and the load on the object.