Damage evolution process (DEP) of concrete can be evaluated by acoustic emission (AE) technology. In order to resonably describe the DEP of concrete, AE test of the whole process of concrete damage under uniaxial and eccentric compressions were carried out and the evolution law of AE characteristic parameters (AECPs) in the whole process of concrete damge were analyzed. Moreover, the optimal AECPs were resonable selected, and the relationship between the characteristic points of stress-strain curve and AECPs was revealed. Results show that the AECPs including counts, duration, amplitude, signal strength and average frequency well describe DEP of concrete. Meanwhile, there is a high correlation between characteristic points of AECPs and stress-strain curve during the compression failure of the concrete specimen. The first demarcation point of AECPs corresponds to the starting point of elastic stage of stress-strain curve, the second demarcation point corresponds to the peak stress point of stress-strain curve, and the maximum mutation point of signal strength corresponds to the cracking point of stress-strain curve.