With the increasing problem of population aging, more and more elderly people are inclined to choose home care. In order to improve the safety and independence of elderly home care, home care robots are viewed as a feasible solution, which can undertake some cumbersome and complex housework tasks. Therefore, this article proposes a novel digital twin system of elderly-care robot (ECRDTS) for housework execution for the first time. Firstly, the architecture of the digital twin system is proposed, which can accurately reflect the characteristics of the physical robot and enable the robot to achieve motion simulation, 3D state monitoring, and virtual-real synchronization. Secondly, ECRDTS was constructed in three dimensions of geometry, data, and robot task execution process, which realized high-fidelity mapping from physical space to digital space and laid the foundation for subsequent robots to autonomously execute housework tasks in a digital twin environment. Finally, the proposed method is applied to the task planning of robot-assisted cleaning of vegetables and fruits in the family kitchen scene, and the effectiveness of the method in practical application scenarios is verified. This research achievement not only meets the needs of elderly home care but also ensures the safety and independence of elderly living alone. Ultimately, this technology is expected to be widely used in nursing homes, hospitals, and home care tasks.