\begin{document}$\sigma_{1}(\omega)$\end{document}, 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 \begin{document}$\sigma_{1}(\omega)$\end{document}, which cannot be described well by the Drude-Lorentz model. Therefore, we introduce a frequency-independent component to fit \begin{document}$\sigma_{1}(\omega)$\end{document} 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 \begin{document}$\sigma_{1}(\omega)$\end{document}. Through calculation and analysis, we attribute the constant component to the surface state of BaMnSb2.">