For preparing a device-quality $CuInSe_2$ (CISe) light-absorbing layer by single-bath electrodeposition for a superstrate-type CISe cell, morphological properties of the CISe layers were investigated by varying concentrations of sulfamic acid and potassium biphthalate, complexing/buffering agents. CISe films were grown on an $In_2Se_3$ film by applying a constant voltage of -0.5V versus Ag/AgCl for 90 min in a solution with precursors of $CuCl_2$, $InCl_3$, and $SeO_2$, and a KCl electrolyte. A dense and smooth layer of CISe could be obtained with a solution containing both sulfamic acid and potassium biphthalate in a narrow concentration range of combination. A CISe layer prepared on the $In_2Se_3$ film with proper concentrations of complexing/buffering agents exhibited thickness of $1.6{\sim}1.8{\mu}m$ with few undesirable secondary phases. On the other hand, when the bath solution did not contain either sulfamic acid or potassium biphthalate, a CISe film appeared to contain undesirable flake-shape $Cu_{2-x}Se$ phases or sparse pores in the upper part of film.