The CaCu3Ti4-xNbxO12(x=0，0.01，0.04，0.08，0.2) ceramics have been prepared by solid-state reaction. The XRD of the sintered ceramics indicated that complete solutions are formed for all compositions x. Dielectric properties have been investigated in the frequency range from 40Hz to 110MHz. Compared with the un-doped CCTO sample，a Debye-type dielectric relaxation has been observed for the Nb-doping CCTO samples in the frequency range from 40Hz to 10kHz at room temperature，apart from the one already known in the frequency range higher than 10kHz. Moreover，the dielectric constant reaches 106 below the characteristic frequency of the lower frequency dielectric relaxation peak which shifts to higher-frequency with increasing Nb content. The experimental results are well explained in terms of the barrier layer capacitance model and an equivalent circuit containing three RC elements by showing three semicircles in the impedance spectroscopic plane.