Simultaneous Localization and Mapping (SLAM) technology enables the construction of environmental maps and localization, serving as a key technique for indoor autonomous navigation of mobile robots. Traditional SLAM methods typically require exhaustive traversal of all rooms during indoor navigation to obtain a complete map, resulting in lengthy path planning times and prolonged time to reach target points. Moreover, cumulative errors during motion lead to inaccurate robot localization, impacting navigation efficiency.This paper proposes an improved SLAM method, FR-SLAM, based on floor plan registration, utilizing a morphology-based floor plan registration algorithm to align and transform original floor plans. This approach facilitates the rapid acquisition of comprehensive motion maps and efficient path planning, enabling swift navigation to target positions within a shorter timeframe. To enhance registration and robot motion localization accuracy, a real-time update strategy is employed, comparing the current position's building structure with the map and dynamically updating floor plan registration results for precise localization. Comparative tests conducted on real and simulated datasets demonstrate that, compared to other benchmark algorithms, this method achieves higher floor plan registration accuracy and shorter time consumption to reach target positions.