Abstract: As an accompanying phenomenon, the acoustic emission of the concrete has memory of the stress-strain history, which could be used to evaluate the concrete damage history. The cyclic tensile failure experiment of the concrete specimen with central crack was conducted. Relationships between parameters of acoustic emission and cyclic loading process were analyzed. The acoustic emission damage mode of concrete under cyclic tension was established. The influence of initial width of crack on the Felicity rate was revealed. The results indicate that the Felicity rate of the concrete prisms gradually increase with the initial width of the crack under dynamic axial cyclic loading. The key outcomes of this article provide a new process of evaluating the concrete damage history with acoustic emission memory.