The robotic manipulation of deformable linear objects (DLOs) has broad application prospects in many fields. However, a key issue is to obtain the exact deformation models (i.e., how robot motion affects DLO deformation), which are hard to theoretically calculate and vary among different DLOs. Thus, the shape control of DLOs is challenging, especially for large deformation control that requires global and more accurate models. In this article, we propose a coupled offline and online data-driven method for efficiently learning a global deformation model, allowing for both accurate modeling through offline learning and further updating for new DLOs via online adaptation. Specifically, the model approximated by a neural network is first trained offline on random data, then seamlessly migrated to the online phase, and further updated online during actual manipulation. Several strategies are introduced to improve the model's efficiency and generalization ability. We propose a convex-optimization-based controller and analyze the system's stability using the Lyapunov method. Detailed simulations and real-world experiments demonstrate that our method can efficiently and precisely estimate the deformation model and achieve the large deformation control of untrained DLOs in 2-D and 3-D dual-arm manipulation tasks better than the existing methods. It accomplishes all 24 tasks with different desired shapes on different DLOs in the real world, using only simulation data for the offline learning.