This paper presents a navigation framework for mobile robots. In order to traverse in different environments, mobile robots have to avoid obstacles it encountered and make a suitable decision with the consideration of global destination. On the basis of grid map provided by the 3D LiDAR, this framework is related to the SLAMs with motion planning methods, where different SLAMs and different planning solutions can be combined to achieve the navigation in dynamic environments. Concretely, the ORB SLAM2 with a slightly improved VFH+ provides a solution, and a navigation method based on Bezier curve with Cartographer SLAM is presented, specifically, we consider the influence area caused by the dynamic obstacle with probabilistic descriptions. The effectiveness is verified by the experiments.