Intraoperative ultrasound facilitates localisation of tumour boundaries during minimally invasive procedures. Autonomous ultrasound scanning systems have been recently proposed to improve scanning accuracy and reduce surgeons’ cognitive load. However, current methods mainly consider static scanning environments typically with the probe pressing against the tissue surface. In this work, a motion-compensated autonomous ultrasound scanning system using the da Vinci® Research Kit (dVRK) is proposed. An optimal scanning trajectory is generated considering both the tissue surface shape and the ultrasound transducer dimensions. An effective vision-based approach is proposed to learn the underlying tissue motion characteristics. The learned motion model is then incorporated into the visual servoing framework. The proposed system has been validated with both phantom and ex vivo experiments.