Global Routing (GR) is a core yet time-consuming task in VLSI systems. It recently attracted efforts from the machine learning community, especially generative models, but they suffer from the non-connectivity of generated routes. We argue that the inherent non-connectivity can harm the advantage of its one-shot generation and has to be post-processed by traditional approaches. Thus, we propose a novel definition, called hub, which represents the key point in the route. Equipped with hubs, global routing is transferred from a pin-pin connection problem to a hub-pin connection problem. Specifically, to generate definitely-connected routes, this paper proposes a two-phase learning scheme named HubRouter, which includes 1) hub-generation phase: A condition-guided hub generator using deep generative models; 2) pin-hub-connection phase: An RSMT construction module that connects the hubs and pins using an actor-critic model. In the first phase, we incorporate typical generative models into a multi-task learning framework to perform hub generation and address the impact of sensitive noise points with stripe mask learning. During the second phase, HubRouter employs an actor-critic model to finish the routing, which is efficient and has very slight errors. Experiments on simulated and real-world global routing benchmarks are performed to show our approach's efficiency, particularly HubRouter outperforms the state-of-the-art generative global routing methods in wirelength, overflow, and running time. Moreover, HubRouter also shows strength in other applications, such as RSMT construction and interactive path replanning.