This paper presents the numerical simulation of the rigid 12.6 mm diameter kinetic energy ogive-nosed projectile impact on plain and fiber reinforced concrete (FRC) targets with compressive strengths from 45 to 235 MPa, using a three-dimensional finite element code LS-DYNA. A combined dynamic constitutive model, describing the compressive and tensile damage of concrete, is implemented. A modified Johnson_Holmquist_Cook (MJHC) constitutive relationship and damage model are incorporated to simulate the concrete behavior under compression. A tensile damage model is added to the MJHC model to analyze the dynamic fracture behavior of concrete in tension, due to blast loading. As a consequence, the impact damage in targets made of plain and fiber reinforced concrete with same matrix material under same impact velocities (650 m/s) are obtained. Moreover, the damage distribution of concrete after penetration is procured to compare with the experimental results. Numerical simulations provide a reasonable prediction on concrete damage in both compression and tension.