The generalization of the end-to-end deep reinforcement learning (DRL) for object-goal visual navigation is a long-standing challenge since object classes and placements vary in new test environments. Learning domain-independent visual representation is critical for enabling the trained DRL agent with the ability to generalize to unseen scenes and objects. In this letter, a target-directed attention network (TDANet) is proposed to learn the end-to-end object-goal visual navigation policy with zero-shot ability. TDANet features a novel target attention (TA) module that learns both the spatial and semantic relationships among objects to help TDANet focus on the most relevant observed objects to the target. With the Siamese architecture (SA) design, TDANet distinguishes the difference between the current and target states and generates the domain-independent visual representation. To evaluate the navigation performance of TDANet, extensive experiments are conducted in the AI2-THOR embodied AI environment. The simulation results demonstrate a strong generalization ability of TDANet to unseen scenes and target objects, with higher navigation success rate (SR) and success weighted by length (SPL) than other state-of-the-art models. TDANet is finally deployed on a wheeled robot in real scenes, demonstrating satisfactory generalization of TDANet to the real world.