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Robots are increasingly being employed for diverse applications where they must work and coexist with humans. The trust in human–robot collaboration (HRC) is a critical aspect of any shared-task performance for both the human and the robot. The study of a human-trusting robot has been investigated by numerous researchers. However, a robot-trusting human, which is also a significant issue in HRC, is seldom explored in the field of robotics. Motivated by this gap, we propose a novel trust-assist framework for human–robot co-carry tasks in this study. This framework allows the robot to determine a trust level for its human co-carry partner. The calculations of this trust level are based on human motions, past interactions between the human–robot pair, and the human’s current performance in the co-carry task. The trust level between the human and the robot is evaluated dynamically throughout the collaborative task, and this allows the trust to change if the human performs false positive actions, which can help the robot avoid making unpredictable movements and causing injury to the human. Additionally, the proposed framework can enable the robot to generate and perform assisting movements to follow human-carrying motions and paces when the human is considered trustworthy in the co-carry task. The results of our experiments suggest that the robot effectively assists the human in real-world collaborative tasks through the proposed trust-assist framework.