Effective searching for target objects in indoor scenes is essential for household robots to perform daily tasks. With the establishment of a precise map, the robot can navigate to a fixed static target. However, it is difficult for mobile robots to find movable objects like cups. To address this problem, we establish an object search framework that combines navigation map, semantic map, and scene graph. The robot updates the scene graph to achieve a long-term target search. Considering the different start positions of the robots, we weigh the distance the robot walks and the probability of finding objects to achieve global path planning. The robot can continuously update the scene graph in a dynamic environment to memorize the position relation of objects in the scene. This method has been realized in both simulation and real-world environments. The experimental results show the feasibility and effectiveness of this method.