Micro-biomimetic robots are designed in such a way that animals are imitated morphologically and kinematically. Such robots have many merits. Firstly, their body size is usually very small such that they can pass narrow passages. Secondly, they commonly have high maneuverability such that they can move freely in very complicated environments. Last but not least, they also have strong environmental adaptability such that they handle different environments. Therefore, microbiomimetic robots have great potential in the applications of many special scenarios. For instance, they can be applied to explore in complex and cluttered environments, or collect information from enemies secretly. Consequently, the research on micro-biomimetic robots has recently drawn many attentions. However, the existing micro-biomimetic robots still face several problems. For instance, the stability of their motion is still low and their visual perception through monocular cameras is rather unreliable. These limitations highly restrict the practical application of the micro-biomimetic robots. To alleviate these problems, this paper presents a new micro-biomimetic crawling robot system. The micro-biomimetic crawling robot is designed to mimic the insect which is referred to as 'Trypoxylus dichotomus'. The robot is equipped with a control system that targets hexapod robots, providing the robot with the ability to move. The control system is developed based on the biological motion regulation mechanism. The proposed robot system also includes a vision system based on brain-inspired simultaneous localization and mapping (SLAM) to provide environmental navigation ability for the microbiomimetic crawling robot. The included brain-inspired SLAM is an improved version of RatSLAM, which is developed mainly inspired by the spatial navigation mechanism in rat's brains. The proposed micro-biomimetic crawling robot system has been verified in both an artificial environment and a real-world indoor environment. The size of the artificial environment is relatively small. Moreover, the environmental image provided by the micro-biomimetic crawling robot was rather blur. Thus, in the artificial environment, the classical ORB-SLAM3 failed to detect the loop closure completely, totally unable to recognize the place which was previously visited. However, the brain-inspired SLAM has obtained a loop closure detection accuracy as high as 100%, being 4.36% higher than the original RatSLAM. In the real indoor corridor scene, the ORB-SLAM3 algorithm and the original RatSLAM algorithm have poor map construction effect, while brainSLAM not only has better map construction results, but also has a recall rate of 97.87% with 100% accuracy. In the realworld indoor environment, compared to ORB-SLAM3 and the original RatSLAM, the brain-inspired SLAM has obtained a much better environmental map, showing the effectiveness of the brain-inspired SLAM. Therefore, the developed microbiomimetic crawling robot system has flexible movement ability and robust positioning capability, pushing the microbiomimetic robots closer to real applications.