An important problem facing stress-strain response modeling of concrete is the complexity of the compressive strength grades. 21 groups of specimens with different cubic compressive strength (56.3-164.9 MPa) have been numerically analyzed. Using only the compressive strength, a stress-strain response model of different concrete grade was established. The numerical simulation model not only quantitatively reproduces the relationship of uniaxial compressive strength, peak value stress and cubic compressive strength, but realizes the consistence of the ascending branch of stress-strain curves with different strength grades by introducing the correction coefficient k. The results indicate k increases gradually from 0 to approximate 1 with the increase of the compressive strength, corresponding to the transition from the paracurve to straight line branch in stress-strain curves. When k is 0, the model is identical to the Hognestad equation. A good agreement with the experiment data was obtained.