We design a two-dimensional photonic crystal coupled-cavity waveguide. Transmission spectra of the waveguide are calculated by using finite-difference time-domain (FDTD) method, and slow light with an average group velocity vg=c/725.93, group refractive index ng=725.93 at the central wavelength of 1.54538 μm is obtained. This coupled-cavity waveguide can produce “U” type group index-frequency curves with low-dispersion slow-light area at the bottom of the “U” type curves, and the central wavelength of the area of 1.54720 μm, average group index g=142.6, bandwidth Δλ=2.16 nm and flat ratio σ=3.20% are obtained by calculation. We shift the location of the first row of air hole in the coupled-cavity waveguide to investigate the change of low-dispersion slow light. The results show that the central wavelength of low-dispersion slow light at the bottom of the “U” type area varies from 1.54720 μm to 1.60549 μm, the average group index g varies from 142.6 to 26.7 and the bandwidth Δλ increases from 2.16 nm to 15.21 nm by shifting the location of the first row of air hole in the coupled-cavity waveguide.