The phenomenon creep fracture is well-known for concrete. In the present paper, the Material Failure Process Analysis (MFPA2D) model for concrete in the failure process is coupled in series with the time-dependence of the concrete damage and deformation. Further, the progressive creep failure of concrete specimens under constant tensile loading was numerically simulated and the typical time-dependent deformations: the transient creep, the steady-state creep and the accelerating creep were also represented. The numerical simulations indicate that the macroscopic creep failure is induced by clusters of micro-fractures on a mesocopic scale. The above numerical results offer us some theoretical indications and instructions to further investigate the instability failure mechanisms of engineering concrete structures in civil and hydraulic engineering.