The image-based visual servoing without models of system is challenging since it is hard to fetch an accurate estimation of hand-eye relationship via merely visual measurement. Whereas, the accuracy of estimated hand-eye relationship expressed in local linear format with Jacobian matrix is important to whole system's performance. In this article, we proposed a finite-time controller as well as a Jacobian matrix estimator in a combination of online and offline way. The local linear formulation is formulated first. Then, we use a combination of online and offline method to boost the estimation of the highly coupled and nonlinear hand-eye relationship with data collected via depth camera. A neural network (NN) is pre-trained to give a relative reasonable initial estimation of Jacobian matrix. Then, an online updating method is carried out to modify the offline trained NN for a more accurate estimation. Moreover, sliding mode control algorithm is introduced to realize a finite-time controller. Compared with previous methods, our algorithm possesses better convergence speed. The proposed estimator possesses excellent performance in the accuracy of initial estimation and powerful tracking capabilities for time-varying estimation for Jacobian matrix compared with other data-driven estimators. The proposed scheme acquires the combination of neural network and finite-time control effect which drives a faster convergence speed compared with the exponentially converge ones. Another main feature of our algorithm is that the state signals in system is proved to be semi-global practical finite-time stable. Several experiments are carried out to validate proposed algorithm's performance.