The visual simultaneous localization and mapping (SLAM) method under dynamic environments is a hot and challenging issue in the robotic field. The oriented FAST and Rotated BRIEF (ORB) SLAM algorithm is one of the most effective methods. However, the traditional ORB-SLAM algorithm cannot perform well in dynamic environments due to the feature points of dynamic map points at different timestamps being incorrectly matched. To deal with this problem, an improved visual SLAM method built on ORB-SLAM3 is proposed in this paper. In the proposed method, an improved new map points screening strategy and the repeated exiting map points elimination strategy are presented and combined to identify obvious dynamic map points. Then, a concept of map point reliability is introduced in the ORB-SLAM3 framework. Based on the proposed reliability calculation of the map points, a multi-period check strategy is used to identify the unobvious dynamic map points, which can further deal with the dynamic problem in visual SLAM, for those unobvious dynamic objects. Finally, various experiments are conducted on the challenging dynamic sequences of the TUM RGB-D dataset to evaluate the performance of our visual SLAM method. The experimental results demonstrate that our SLAM method can run at an average time of 17.51 ms per frame. Compared with ORB-SLAM3, the average RMSE of the absolute trajectory error (ATE) of the proposed method in nine dynamic sequences of the TUM RGB-D dataset can be reduced by 63.31%. Compared with the real-time dynamic SLAM methods, the proposed method can obtain state-of-the-art performance. The results prove that the proposed method is a real-time visual SLAM, which is effective in dynamic environments.