We report on spectral-domain and time-domain measurements and numerical calculations of group velocities in a photonic crystal coupled waveguide, where the unique guided mode band structure has a flat band region within the photonic band gap allowing for slow light observation. The spectral dependence of group velocity, which is measured by interference method, indicates the existence of slow light modes around the inflection point of the unique flat band, rather than at the band edge. Time-domain observation of optical pulses propagating along two-dimension slab photonic crystal coupled waveguides is also demonstrated by using a high speed oscilloscope. By adjusting the wavelength of the input pulses toward the flat band of the coupled defect modes, an increasing duration time between reference and output pulses are clearly observed. An extremely small group velocity of 0.017c is thus obtained. Calculated group velocities show good agreement with our measured results.