Acoustic emission signals from concrete compression damage process are non-stationary and their arrival time is unknown. Therefore, the definition on the acoustic emission event in the time series is not clear. In this paper, the acoustic emission signals associated with concrete specimen under uniaxial compression are acquired by full-digital acoustic emission system. The overlapping phenomenon of acoustic emission signal is presented and discussed by the analysis of time interval between adjacent hits. Acoustic emission signals are classified into three categories according to their waveform characteristics. And the result shows that as the loading process continues, more and more amount of continuous type of acoustic emission signals appeared, indicating the acoustic emission signal does not carry the features of burst type, which will introduce obvious errors in the calculation of acoustic emission event. In contrast, the average signal level used in the analysis of continuous type of acoustic emission signal shows a good regularity with the damage process of concrete.