Robotic ultrasound scanning has excellent potential to reduce physician workload, obtain higher-quality imaging, and reduce costs. However, the traditional admittance control strategy for robotics cannot meet the high-precision force control requirements for robots, which are critical for improving image quality and ensuring patient safety. In this study, an integral adaptive admittance control strategy is proposed for contact force control between an ultrasound probe and human skin to enhance the accuracy of force tracking. First, a robotic ultrasound scanning system is proposed, and the system’s overall workflow is introduced. Second, an adaptive admittance control strategy is designed to estimate the uncertain environmental information online, and the estimated parameters are used to modify the reference trajectory. On the basis of ensuring the stability of the system, an integral controller is then introduced to improve the steady-state response. Subsequently, the stability of the proposed strategy is analysed. In addition, a gravity compensation process is proposed to obtain the actual contact force. Finally, through a simulation analysis, the effectiveness of the strategy is discussed. Simultaneously, a series of experiments are carried out on the robotic ultrasound scanning system, and the results show that the strategy can successfully maintain a constant contact force under soft uncertain environments, which effectively improves the efficiency of scanning.