Visual servo control rules that refer to the control methods of robot motion planning using image data acquired from the camera mounted on the robot have been widely applied to the motion control of robotic arms or mobile robots. The methods are usually classified as image-based visual servo, position-based visual servo, and hybrid visual servo (HVS) control rules. Mobile manipulation enhances the working range and flexibility of robotic arms. However, there is little work on applying visual servo control rules to the motion of the whole mobile manipulation robot. We propose an HVS motion control method for a mobile manipulation robot which combines a six-degree-of-freedom (6-DOF) robotic arm with a nonholonomic mobile base. Based on the kinematic differential equations of the mobile manipulation robot, the global Jacobian matrix of the whole robot is derived, and the HVS control equation is derived using the whole Jacobian matrix combined with position and visual image information. The distance between the gripper and target is calculated through the observation of the marker by a camera mounted on the gripper. The differences between the positions of the markers' feature points and the expected positions of them in the image coordinate system are also calculated. These differences are substituted into the control equation to obtain the speed control law of each degree of freedom of the mobile manipulation robot. To avoid the position error caused by observation, we also introduce the Kalman filter to correct the positions and orientations of the end of the manipulator. Finally, the proposed algorithm is validated on a mobile manipulation platform consisting of a Bulldog chassis, a UR5 robotic arm, and a ZED camera.