Reducing the cumulative error is a crucial task in simultaneous localization and mapping (SLAM). Usually, Loop Closure Detection (LCD) is exploited to accomplish this work for SLAM and robot navigation. With a fast and accurate loop detection, it can significantly improve global localization stability and reduce mapping errors. However, the LCD task based on point cloud still has some problems, such as over-reliance on high-resolution sensors, and poor detection efficiency and accuracy. Therefore, in this paper, we propose a novel and fast global LCD method using a low-cost 16 beam Lidar based on "Simplified Structure". Firstly, we extract the "Simplified Structure" from the indoor point cloud, classify them into two levels, and manage the "Simplified Structure" hierarchically according to its structure salience. The "Simplified Structure" has simple feature geometry and can be exploited to capture the indoor stable structures. Secondly, we analyze the point cloud registration suitability with a pre-match, and present a hierarchical matching strategy with multiple geometric constraints in Euclidean Space to match two scans. Finally, we construct a multi-state loop evaluation model for a multi-level structure to determine whether the two candidate scans are a loop. In fact, our method also provides a transformation for point cloud registration with "Simplified Structure" when a loop is detected successfully. Experiments are carried out on three types of indoor environment. A 16 beam Lidar is used to collect data. The experimental results demonstrate that our method can detect global loop closures efficiently and accurately. The average global LCD precision, accuracy and negative are approximately 0.90, 0.96, and 0.97, respectively.