CaCu3Ti4O12 ceramic has drawn much attention due to its stable colossal dielectric permittivity and pronounced nonlinear electrical characteristics. In this work, the effects of direct current degradation on the dielectric response and electrical property of CaCu3Ti4O12 ceramic aged for 60 h under 3.5 kV/cm are investigated. The results of J-E characteristic analysis show that the breakdown field E1mA decreases from 216 V/mm to 144 V/mm and nonlinear coefficient η decreases from 4.1 to 2.1. The barrier heights of CaCu3Ti4O12 ceramics are calculated to be in a range of 293-368 K, based on the J-E curves, which decrease from 0.57 eV to 0.31 eV. It is found that the dielectric constant and dielectric loss at low frequencies are significantly increased. Based on Debye function, it is indicated that the dielectric loss is composed of direct current conductance loss and relaxation loss, especially the direct current conductance loss is enhanced by the direct current degradation. At 233 K, two relaxation peaks whose activation energies are 0.10 eV and 0.50 eV can be found, which are considered to be related to grain and domain boundary and not vary with direct current degradation. Electric modulus spectra are used to characterize the role of direct current degradation in the relaxation process of CaCu3Ti4O12 ceramic. The results show that the variation of interfacial space charges caused by direct current degradation obeys the Maxwell-Wagner polarization. It may be a key factor to lead to the increase of dielectric permittivity below 10 Hz, and a new corresponding relaxation peak θ can be observed in the modulus plot at low frequency. In the impedance spectra in 323-473 K, the relaxation peaks of grain boundary shift toward high frequency after direct current degradation. The results from the complex impedance plane show that the resistance of the grain boundary decreases by about two orders of magnitude and its activation energy drops off from 1.23 eV to 0.72 eV, while the resistance of grain decreases a little and its activation energy has no obvious variation. Therefore, it is proposed that direct current degradation should play an important role in grain boundary and affect its electrical property and dielectric response. An RC circuit model is proposed to elucidate the correlation between dielectric relaxation and electrical property of CaCu3Ti4O12 ceramic.