This paper presents a new Simultaneous Localization and Mapping (SLAM) framework for solving the problem of SLAM in dynamic environments. The landmark location change causes the error of robot pose estimation and landmark mapping. In this paper, we propose the Dynamic Extended Kalman Filter (EKF) SLAM based on the independence of the dynamic landmarks. The proposed framework decomposes the SLAM problem into a traditional SLAM problem for the static landmarks and individual SLAM problems for the dynamic landmarks. Therefore, in the dynamic environments, it is able to minimize the error caused by the dynamic landmarks and reduce the uncertainty in the robot pose and the landmark locations. In order to validate the proposed approach, we implement an indoor mobile robot platform with a Red Green Blue - Depth (RGB-D) sensor and utilize Speeded Up Robust Features (SURF) algorithm to extract appearance-based features. The simulation and experimental results show the validity and robustness of the Dynamic EKF SLAM in indoor environments including the dynamic landmarks.