To address the problems of conventional LiDAR simultaneous localization and mapping (SLAM) in dynamic environments with large cumulative errors in pose estimation and dynamic object error point clouds in the map, this paper presents a tightly coupled LiDARinertial SLAM (DM-LIO) method for real-time removal of dynamic objects based on the visible point method. This method by utilizes the IMU measurements to provide a priori poses for the dynamic object removal module based on the visible point method, and also introduces a point cloud clustering method based on curved voxel space to solve the problem that dynamic points of viewable point method cannot be fully captured at low resolutions, which enables the rejection of dynamic objects in laser point clouds at the front end of algorithm. The performance of algorithm is evaluated by both building a real indoor experimental platform and using a public dataset. The results of real-world experiments show that the proposed DM-LIO method is able to remove multiple dynamic objects as well as non-a priori dynamic objects online; the test results based on the public dataset of Urbanloco show that the absolute trajectory error of DM-LIO is reduced by more than 60% compared to LIO-SAM in highly dynamic environments, which verifies that the algorithm possesses good positioning accuracy in a highly dynamic environment.