In visual servoing tasks, it is an important problem to maintain the observability to feature points on objects, which are usually used to calculate the pose between objects and robots. In particular, when the robot's vision has a limited field of view (FOV) and the points on objects are distributed separately, the problem is more serious. In this paper, based on FOV constraint region analysis and path planning, we propose a novel method for a mobile robot equipped with a pan-tilt camera to keep all points on objects in its view. According to the Horizontal-FOV and Vertical-FOV angular aperture of camera, bounding boxes assisting to calculate the regions with FOV constraint are acquired firstly. Then the region where the robot inside it cannot keep all points in its view can be obtained. Finally the mobile robot plans a shortest path from the current position to the destination, which can avoid the region with FOV constraint. The results of simulations and experiments prove that our method can make mobile robot keep all feature points in its view when it is moving.