Starting from the Maxwell's equation, and using the resonant-dipole equation together with the multilevel rate equations which take the effects of energy relaxation into consideration, we have derived a more realistic numerical model of the chirped pulse amplification for an ultra-broad band width laser amplifier. Numerical simulations of this model show that both the intensity profile and the energy fluence of the amplified chirped pulse are closely connected with the two relaxation effects: the relaxation of the thermalization among the components of the laser multiplets and the depletion of the lower laser level. The results are valuable for the design of ultra-broad bandwidth chirped pulse amplification lasers.