An ab-initio pseudopotential calculation has been performed by using density functional methods within the local density approximation (LDA) to investigate the band structure and optical properties of the ferroelectric-semiconductor SbSI in the para-and ferroelectric phases. It has been shown that SbSI has an indirect gap in both phases (1.45 eV and 1.49 eV in the para-and ferroelectric phases respectively) and that the smallest direct gap is at the S point of the Brillouin zone (1.56 eV and 1.58 eV in the para-and ferroelectric phases respectively). Furthermore, it is shown that first-order phase transition, from the paraelectric phase to the ferroelectric phase (the transiton temperature is about 22 o C), does not change the nature of the band gap. Moreover, the linear frequency dependent dielectric function, including self-energy effects, has been calculated along the c-polar axis in the para-and ferroelectric phases.