Tactile sensation endows humans with the capacity to localize objects, which is also significant for robots. However, it is challenging for robots to localize and grasp objects only by tactile sensation. One potential snag is that tactile sensors do not provide feedback without external contact, which means the robot cannot spontaneously plan its path. To address this issue, we propose a novel Virtual Tactile POMDP (VT-POMDP)-based method for object localization and grasping in a 3D workspace, which models the path planning problem as the VT-POMDP to plan the motion path of the grasper. The state space and action space in the VT-POMDP are classified into seven categories to reduce the spatial dimension and the computational cost of path planning. Furthermore, we model the motion scale of the grasper using a variable-scale moving strategy to improve the efficiency of object localization. Finally, we verify the effectiveness and generalization of the method through a series of simulation experiments and real-world experiments.