In the application of visual navigation, submap-based VSLAM has become one of the most robust monocular solutions in recent years, which is able to resume tracking by multi-submap maintenance and merging. However, due to the lack of long-term data association, the global consistency of submaps cannot be guaranteed in the existing work. Considering the fact that long-term data association does not have to be produced in realtime, we propose a VSLAM system with realtime and non-realtime hybrid style, RUMI-SLAM. Inspired by the rumination of mammalians that processes food in various stomaches and absorbs it in one stomach, RUMI-SLAM performs distributed submap building and centralized submap management. Building additional submaps in parallel leads to enriched mapping elements and enhanced data association across submaps, especially in challenging situations such as interleaved blurry and texture-poor frames. The experimental results demonstrate the superiority of RUMI-SLAM over the existing VSLAM systems, especially the robustness to challenging situations. We also provide real-robot experiments to demonstrate our RUMI-SLAM in the application of visual navigation. Our study provides a novel submap-based VSLAM framework, which achieves a robust and globally consistent performance.#This paper has been accepted by IEEE TIE