A graded band-gap CuInSe2 (CIS) thin film solar cell (TFSC) having glass/FTO/CdS/CIS multilayer/Au structure has been fabricated. A simple and low-cost electrodeposition technique is used to deposit the multilayers of CIS onto fluorine doped tin oxide (FTO) coated glass substrate. A conventional three-electrode geometry consisting, FTO, graphite and Ag/AgCl as a working, counter and reference electrodes, respectively was used for electro-deposition. Structural characterization was carried out using X-ray diffraction (XRD) and Raman spectroscopy, which revealed the chalcopyrite tetragonal CIS structure with a quite Cu-rich surface which reduces upon selenization. The morphology of the as grown and selenized CIS multilayer thin films was studied by using atomic force microscopy (AFM) which shows the compact and uniform layer formation. The depth profile distribution of individual elements in both as-grown and selenized CIS multilayer thin films has been determined using secondary ion mass spectroscopy (SIMS). SIMS results revealed that the proposed graded band gap structure is retained even after selenization. The presence of Cu+, In3+ and Se2- oxidation states were confirmed using X-ray photoelectron spectroscopy (XPS). A single layer and multilayer CIS solar cell devices yielded similar to 5.10% and similar to 7.20% power conversion efficiency, respectively. In the present work, pH 3 buffer solution helps to improve the morphology of CIS layer which gives the better power conversion efficiency as compared to the previously reported value.