A detailed infrared optical spectrum of the new topological material BaMnSb ₂has been measured at temperatures ranging from 7 K to 295 K. As the temperature decreases, the plasma minimum has a clear blue shift in reflectivity spectrum, indicating that the carrier density changes with temperature. In the real part of the optical conductivity $\sigma_{1}(\omega)$ , two linearly-increased components can be identified, but neither of their extrapolation pass through the origin, which proves that BaMnSb ₂has a gapped Dirac dispersion near the Fermi level. Comparing with the theoretical calculation by using first-principles methods, the onset of these two linearly-increased components are in good agreement with the band structures. In addition, a range of constant optical conductivity is found in $\sigma_{1}(\omega)$ , which cannot be described well by the Drude-Lorentz model. Therefore, we introduce a frequency-independent component to fit $\sigma_{1}(\omega)$ successfully. However, different from the Dirac nodal-line semimetal YbMnSb ₂which shares same fitting results as well as crystal structure, the constant component in BaMnSb ₂has a small proportion of $\sigma_{1}(\omega)$ . Through calculation and analysis, we attribute the constant component to the surface state of BaMnSb ₂.