The fundamental theory of the fission-track thermochronology has been based on the principle that temperature is the only factor of fission track annealing. However, whether the radiation damage can enhance the annealing or not remains in dispute. This work studies the relationship between radiation damage and the fission track annealing behavior by the apatite fission track dating of four granite samples from Lincang county in Yunnan province. The single grain fission track ages of the samples range from 71 Ma to 15 Ma. The confined track lengths of the samples range from 9 μm to 16 μm and the U concentrations of the samples range from 24 μg/g to 290 μg/g. The analytical results of the relationship between fission track age and length and U concentration show that the fission track age and length decrease wirh increasing U concentration. The relationship preliminarily indicates that the radiation damage could cause and enhance fission track annealing as another factor in addition to temperature. This observation provides evidence for studing fission track annealing behavior caused by radiation damage.