MgSe/ZnCdSe superlattices (SLs) and n-MgZnCdSe quaternaries were investigated as an n-cladding layer material of II-VI compound semiconductor optical devices on InP substrates. n-type samples consisting of n-doped ZnCdSe and n-MgSe/ZnCdSe SL or n-MgZnCdSe layers were fabricated on n-InP substrates by molecular beam epitaxy. From the injection current density versus applied voltage (J-V) characteristics of the samples, it was found that the applied voltage and resistivity of the MgZnCdSe sample were lower than those of the SL sample. This shows that MgZnCdSe is more suitable for the n-cladding layer. On the other hand, Schottky characteristics were observed for both samples, which were ascribed to conduction band hetero-barriers between the n-ZnCdSe and the SL or MgZnCdSe layers. The Schottky characteristics cause high applied voltages of the II-VI optical devices. To solve this problem (i.e., the Schottky characteristics), the incorporation of ZnCdSe/MgZnCdSe graded SLs at the interface between the n-ZnCdSe and MgZnCdSe layers was proposed. From the J-V characteristics, it was confirmed that the Schottky characteristics and applied voltages were reduced by introducing the graded SLs. This shows that the graded SLs are effective for lowering the applied voltages of II-VI optical devices on InP substrates.