In this paper, some numerical tests on the fracture process zone (FPZ) in concrete tension specimen were carried out with Material Failure Process Analysis code (MFPA2D) to investigate the behavior of the FPZ and the effect of the meso-scale heterogeneity of concrete on fracture process. The numerical results provide a clear indicator of the FPZ of concrete. The numerical results show that the FPZ accompanied by AE events gradually develops ahead of the notch tip with the increase of the loading in the concrete tension specimen. Moreover, many of the AE events bring about very small energy at the beginning of loading stage. Zones of higher energy events demonstrate a localization zone around the notch tip. The zones of AE events progresses forward gradually, and much densely distributed AE events can be observed in the FPZ. Moreover, the numerical simulations about AE events agreed well with those of the microcracks obtained by laboratory findings.