Object grasping is an important ability required for various robot tasks. In particular, tasks that require precise force adjustments during operation, such as grasping an unknown object or using a grasped tool, are difficult for humans to program in advance. Recently, AI-based algorithms that can imitate human force skills have been actively explored as a solution. In particular, bilateral control-based imitation learning achieves human-level motion speeds with environmental adaptability, only requiring human demonstration and without programming. However, owing to hardware limitations, its grasping performance remains limited, and tasks that involves grasping various objects are yet to be achieved. Here, we developed a cross-structure hand to grasp various objects. We experimentally demonstrated that the integration of bilateral control-based imitation learning and the cross-structure hand is effective for grasping various objects and harnessing tools.