Observations using a narrow band H alpha filter still remain one of the best ways to investigate the fine structures and internal dynamics of solar filaments. H alpha observations, however, have been usually carried out with the peak response of the filter fixed at a single wavelength, usually at the centerline, in which the investigation is limited to the H alpha morphology and its time evolution. In this paper, we demonstrate that the H alpha spectroscopy that takes H alpha images successively at several wavelengths is a useful tool in the study of solar filaments on the solar disk. Our observation of a filament was carried out on August 3, 2004 at Big Bear Solar Observatory using the 10-inch refractor. The Lyot H alpha filter was successively tuned to five wavelengths: -0.6, -0.3, 0.0, +0.3, and +0.6 angstrom from the H alpha line center. Each set of wavelength scan took 15 s. After several steps of data reduction, we have constructed a five-wavelength spectral profile of intensity contrast at every spatial point. The contrast profile at each spatial point inside the filament was reasonably well fit by the cloud model as far as the contrast is high enough, and allowed us to construct the maps of tau(0), nu, Delta lambda(D) and S in the filament. We also found that the line center method that is often used, always yields line-of-sight velocities that are systematically lower than the cloud model fit. Our result suggests that taking H alpha images at several wavelengths using a tunable filter provides an effective way of deriving physically meaningful parameters of solar filaments. Particularly constructing the time sequence of v maps appears to be a useful tool for the study of internal dynamics, like counterstreaming, in filaments.