To reveal the influence mechanism of initial temperature damage on the failure characteristics of granite rockburst, the true triaxial strainburst experiments were carried out on granite samples experiencing different initial damage temperatures. First, the peak strength and failure intensity evaluated by the rockburst pit volume of the granite samples were investigated. Second, by calculating the fractal dimensions of the rockburst fragments, the impacts of the initial temperature damage on the scale parameters, surface morphology and microscopic cracks of the rockburst fragments were quantitatively analyzed. Finally, on the basis of the crack evolution characteristics inside the samples during rockburst, a link between the peak strength of the rockburst and the fractal dimension of the fragments was established. The results indicated that with increasing initial damage temperature, the peak strength and failure intensity of rockburst for granite samples initially increase and subsequently decrease. The samples experiencing an initial damage temperature of 200 ℃ present the highest fractal dimensions of scale parameters, surface morphology and microscopic cracks of rockburst fragments, indicating that 200 ℃ is the temperature threshold that affects the failure intensity of rockburst and the fragmentation degree of fragments. The peak strength of rockburst failure for granite samples experiencing different initial damage temperatures is positively correlated with the fractal dimensions of rockburst fragments, providing a scientific basis for revealing the incubation and evolution mechanism of granite samples during rockburst.