This study investigated the crystal growth, crystalline structure and the basic optical properties of $SnSe/BaF_2$ epilayers. The SnSe epilayer was grown on $BaF_2$(111) insulating substrates using a hot wall epitaxy(HWE) technique. It was found from the analysis of X-ray diffraction patterns that $SnSe/BaF_2$ epilayer was growing to single crystal with orthorhombic structure oriented [111] along the growth direction. Using Rutherford back scattering(RBS), the atomic ratios of the SnSe was found to be stoichiometric, almost 50 : 50. The best values for the full width at half maximum (FWHM) of the DCXRD was 163 arcsec for SnSe epilarer. The epilayer-thickness dependence of the FWHM of the DCXRD shows that the quality of the $SnSe/BaF_2$ is as expected. The dielectric function ${varepsilon}$(E) of a semiconductor is closely related to its electronic energy band structure and such relation can be drawn from features around the critical points in the optical spectra. The real and imaginary parts(${varepsilon}_1$ and ${varepsilon}_2$) of the dielectric function ${varepsilon}$ of SnSe were measured. These data are analyzed using a theoretical model known as the model dielectric function(MDF). The optical constants related to dielectric function such as the complex refractive index(n*-n+ik), absorption coefficient (${alpha}$) and normal- incidence reflectivity (R) are also presented for $SnSe/BaF_2$.