Due to the intermittent motion of a legged mobile robot, an additional periodic movement must be introduced that directly affects the image processing accuracy and destabilizes the visual servo control of the robot. To address this problem, this paper investigates a control scheme for the visual servoing of a legged mobile robot equipped with a fixed monocular camera. The kinematics of the legged mobile robot and homography- based visual servoing are employed to allow the robot to achieve the desired pose. By investigating the homographic relationship between the current and desired poses, the approach has no need for transcendental knowledge of the three-dimensional geometry of the target image. The feature points are directly extracted from the images to evaluate the homography matrix. To reduce the effects caused by the intermittent motions of the legged robot, an improved adaptive median filter is proposed. Furthermore, a sliding mode controller is designed, and a Lyapunov-based approach is used to analyze the stability of the control system. With the aid of CoppeliaSim software, a simulation is implemented to verify the effectiveness of the proposed method.