To objectively evaluate the whole process of transport-reaction-damage of concrete under sulfate attack, a transport model considering porosity, tortuosity and critical damage degree is established based on the theory of crystallization pressure, volume expansion theory and Fick's second law. Meanwhile, the variable coefficient of sulfate transport is solved by alternating implicit difference method. Results show that the prediction results are basically consistent with the experiment. The model can better predict the diffusion law of sulfate ions in concrete, with a maximum error of 28.6%. The influence factors analysis shows that the concentration of sulfate attack and the critical damage degree present a great influence on the spalling thickness of concrete cover. Under the same critical damage degree, the spalling speed increases with the sulfate concentration. It shows that the spalling speed in 5% sodium sulfate solution is 133.0% faster than that in 1% sodium sulfate solution. Under the same concentration of sodium sulfate solution, the spalling thickness decreases with the critical damage degree. When the critical damage degree increases from 0.8 to 0.95, the spalling thickness decreases by 42.9%.