A 2D model is developed to investigate the grain growth behavior under the influence of temperature gradient using the phase field method. The model is used to simulate the effect of temperature gradient on the nonuniform and directional grain growth behavior during annealing of polycrystalline materials. The results show that the static temperature gradient leads to the nonumiform grain growth, and that the grain growth exponent deviates from that of normal grain growth. In the case of annealing with a moving temperature gradient, the columnar grains may develop towards the locations with the highest temperature in the heated zone. Moreover, the grain growth behavior is closely related to the moving speed of the moving heated zone. Columnar grains occur only when the moving speed of the heated zone is higher than the minimum grain growth rate but lower than the maximum grain growth rate.