Nonlinear optical single crystals of L-cystine dihydrobromide (LCHB) have been grown by slow evaporation method. Single crystal X-ray diffraction analysis revealed the crystal system and lattice parameter values. Powder X-ray diffraction analyses have been carried out and the diffraction patterns have been indexed. Fourier transform infrared (FTIR) analysis confirms the various functional groups present in the grown crystal. The thermal behavior of the grown crystal was investigated by DTA and TGA analysis. The optical properties of the crystals were determined using UV-Visible transmittance spectrum. The dielectric constant and dielectric loss of the crystal are studied as a function of frequency for various temperatures. The SHG efficiency of the crystal is studied using the Kurtz and Perry technique.