Numerical simulation has been carried out to investigate the influence of radial temperature gradient on the Taylor Vortex flow. Varying the Grashof number, we study the detailed flow and temperature fields. The current numerical results show good agreement with the experimental results currently available. It turns out that wavy spiral vortices are generated by increasing temperature gradient. We classify flow patterns for various Grashof numbers based on the characteristics of flow fields and spiral vortices. The correlation between Grashof number with wave number shows that the spiral angle and size of Taylor vortices increase with increasing temperature gradient. Temperature gradient does not have a great influence on the heat transfer rate of the cylinder surfaces.