$alpha$--sulfur single crystal which has orthorohmbic structure was grown using Bridgman method. The indirect optical energy band gap of this crystal are 2.65 and 2.82 eV at 10 and 300K, respectively. The wavelengths of photoluminecence(PL) peaks are 543 and 596 nm at 10k, By thermally stimulated current (TSC) method, two electron traps($D_1,D_2$) located at 0/23 and 0.43eV below the conduction band and a hole trap(A) located at 0.31 eV above the valence band are observed. PL mechanism of $alpha$-sulfur single crystal is analyzed using the values of optical energy band gap at 10k two electron traps and a hole trap.