This paper presents a novel method for grasping objects with varying stiffness using an underactuated hand and a stereo camera. In factories, robots are required to handle a wide variety of objects. Tasks such as grasping soft objects without causing damage are particularly important in industries like food processing. While many existing approaches equip robotic hands with sensors, such as force or pressure sensors, these methods are unsuitable for food items due to hygiene concerns. To address the challenges of grasping various objects without causing damage or dropping them, underactuated hands that can conform to object shapes have gained attention. In this study, we propose a method for controlling an underactuated hand using only a stereo camera as an external sensor. First, the target object is detected using a background subtraction method. Next, the contact between the hand and the object is detected. Then, the object is grasped with appropriate force, calculated based on four elements: the centroid shifts of the hand and the object, the deformation rate of the object, and the occlusion rate of the hand. Finally, drop detection is performed to ensure the object is not dropped during pick-and-place tasks. Experiments were conducted using six different objects to validate the proposed method.