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Neural scene representation and rendering methods have shown promise in learning the implicit form of scene structure without supervision. However, the implicit representation learned in most existing methods is non-expandable and cannot be inferred online for novel scenes, which makes the learned representation difficult to be applied across different reinforcement learning (RL) tasks. In this work, we introduce Scene Memory Network (SMN) to achieve online spatial memory construction and expansion for view rendering in novel scenes. SMN models the camera projection and back-projection as spatially aware memory control processes, where the memory values store the information of the partial 3D area, and the memory keys indicate the position of that area. The memory controller can learn the geometry property from observations without the camera's intrinsic parameters and depth supervision. We further apply the memory constructed by SMN to exploration and navigation tasks. The experimental results reveal the generalization ability of our proposed SMN in large-scale scene synthesis and its potential to improve the performance of spatial RL tasks.