This paper presents a visual servoing and compliant motion control design of a continuum robot. Two endoscopic cameras were installed at the tip of the continuum robot to build a stereo camera system. The depth information is obtained by using semi-global block-matching (SGBM) algorithm. The visual servoing system proposed in this work includes the feature point extraction by using speeded-up robust features (SURF), followed by feature-point matching using nearest neighbor distance ratio (NNDR), and tracking of feature points by using mean shift algorithm. Through the pressure sensor installed around the circumference of the continuum robot, a compliant motion control design is proposed to make the robot to move in a constrained environment while executing the visual servoing task. Practical experiments show that the proposed method can effectively track a target and generate the adaptive motion when the robot encounters an obstacle during visual servoing.