The study of Taylor-Couette vortex flow with small aspect ratio is great interesting. Additionally, the importance of magnetic fluids has been increasing in the engineering applications of various fields, and this leads to increase the interests to investigate the flow of magnetic fluids, which have the reactivity to magnetic field. Then Taylor-Couette vortex flow with magnetic fluids is expected to control the flow pattern and the mode bifurcation by using magnetic field. Recently, the velocity information of various flow fields is available by using Ultrasonic Velocity Profiler (UVP). Hence, the method for investigating the flow fields in the magnetic fluids has also been available. In this study, the flow structure of a magnetic fluid in a concentric annular geometry with an aspect ratio of 3 and a radius ratio of 0.6 was investigated for an inner cylinder rotation. Axial velocity distributions of the flow field were measured using the UVP measuring technique. In the UVP measurement, an ultrasonic with basic frequency of 8MHz and beam diameter of 3mm was used. A non-uniform magnetic field was applied to the flow field using a permanent magnet located on the outside of the vessel, and the transitions of flow field with a magnet were investigated by using UVP.