A detailed infrared optical spectrum of the new topological material BaMnSb₂ has 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 BaMnSb₂ has 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 YbMnSb₂ which shares same fitting results as well as crystal structure, the constant component in BaMnSb₂ has a small proportion of \sigma_1(\omega). Through calculation and analysis, we attribute the constant component to the surface state of BaMnSb₂.