Under China’s Intelligent Electric Power Grid (IEPG), the research on IEPG inspection mode is of great significance. This work aims to improve the positioning and navigation performance of IEPG inspection robots in a complex environment. First, it reviews the monocular camera projection and the Inertial Measurement Unit (IMU) models. It also discusses the tight-coupling monocular Vision Inertial Navigation System (VINS) and the initialization theory of the Simultaneous Localization and Mapping (SLAM) system. Nonlinear optimization for SLAM by the Gauss–Newton Method (GNM) is established. Accordingly, this work proposes the SLAM system based on tight-coupling monocular VINS. The EuRoC dataset data sequence commonly used in visual-inertial algorithm testing in IEPG is used for simulation testing. The proposed SLAM system’s attitude and position estimation errors are analyzed on different datasets. The results show that the errors of roll, pitch, and yaw angle are acceptable. The errors of the X, Y, and Z axes are within 40 cm, meeting the positioning requirements of an Unmanned Aerial Vehicle (UAV). Meanwhile, the Root Mean Square Error (RMSE) evaluates the improvement of positioning accuracy by loop detection. The results testify that loop detection can reduce the RMSE and improve positioning accuracy. The attitude estimation tests the angle changes of pitch, roll, and yaw angles with time under a single rotation condition. The estimated value of the proposed SLAM algorithm is compared with the real value through Absolute Trajectory Error (ATE). The results show that the real value and the estimated value of attitude error can coincide well. Thus, the proposed SLAM algorithm is effective for positioning and navigation. ATE can also be controlled within ±2.5°, satisfying the requirements of navigation and positioning accuracy. The proposed SLAM system based on tight-coupling monocular VINS presents excellent positioning and navigation accuracy for the IEPG inspection robot. The finding has a significant reference value in the later research of IEPG inspection robots.