It is difficult to estimate the relationship between the motion of joint and the motion of image features, making the Calibration-free visual servoing control challenging. In traditional methods, the hand-eye relationship is usually approximated in purely online or offline ways. A practical scheme for robot arm manipulation with both online and offline learning is proposed in this paper. The hand-eye relationship is formulated in a local linear format with Jacobian matrix, which is approximated by radial-basis function network (RBFN). Primitively, the RBFN is trained offline to form a relatively appropriate estimation of the Jacobian matrix, which is the beginning of the online step. Then, an online modification of the RBFN is executed, compensating the error caused by changes of camera's position and pose or insufficient training. The simulation experiments show that the proposed scheme can provide a reliable offline trained model and can adapt well to the changes of camera's position and pose due to the online update law.