Undoped and Zn-doped SnS nanostructures have been successfully synthesized through an electrodeposition process by using SnCl2 and Na2S2O3 as precursors on fluorine-doped tin oxide-coated (FTO) glass substrates with different zinc concentrations. The structure, surface morphology, and the optical properties of the synthesized films are studied. The X-ray diffraction patterns of the SnS nanostructure confirm the orthorhombic structure. Scanning electron microscopy shows thin films with homogeneous and uniform surface as well, by adding Zn ions, morphology of SnS films changed from cubic to rod. Energy dispersive spectroscopy shows presence of Zn in the films. All samples are characterized by UV-Vis reflectance measurement in the wavelength range 500-1200 nm. The energy band gap values, calculated from optical measurement of reflectance, are between 1.46 and 1.49 eV, being suitable for absorbers layers in the photovoltaic applications. Eventually, studying the photocurrent responses of the nanostructures revealed that the Zn-doped SnS nanostructures exhibited better response than the undoped SnS nanostructures.