In the frame of the constituent quark model with screened color confinement, non-strange baryon spectra are studied by using non-relativistic and semi-relativistic Faddeev equations in momentum space. The results show that a qualitative description of the high-energy baryon spectra can be obtained, especially for states at excitation energies from 1 to 1.5GeV. Compared with the linear confinement potential, the discrepancy between non-relativistic and semi-relativistic approaches becomes smaller in the present model with screened color confinement.