The present study investigates the barotropic vortex motion over topography on a b plane by an analytical vortex track model and a high resolution shallow water model. Under the assumptions of constant vorticity and constant vortex depression at the vortex center at a small time instance, we derive a so-called meridional adjusting velocity (MAV) and a topographic adjusting velocity (TAV) for the vortex motion from the conservation of potential vorticity. These two vortex adjusting velocities are generated associated with the vortex motion driven by the planetary b effect as well as the steering flow effect. A detailed parameteric investigation of the dynamic model explores the track dynamics of the vortex over a north-south ridge or an elliptic-shape mountain. Their topographic parameters are decided to adequately represent the conditions of the problem of typhoons encountering the Taiwan's CMR. Three significant types of vortex drifting are discovered including the type of deceleration-acceleration (type of 'D-A'), the type of 'D-A-D-A', and the type of 'A-D' associated with the vortex acrossing the topography. The vortex tracks predicted from the dynamic model are very similar to those obtained from the shallow water simulations as well as some historical events of typhoons encountering the CMR of Taiwan.