Dependence of band alignments at interfaces between CdS by chemical bath deposition and Cu(In1-xGax)Se2 by conventional 3-stage co-evaporation on Ga substitution ratio x from 0.2 to 1.0 has been systematically studied by means of photoemission spectroscopy (PES) and inverse photoemission spectroscopy (IPES). For the specimens of the In-rich CIGS, conduction band minimum (CBM) by CIGS was lower than that of CdS. Conduction band offset of them was positive about +0.3 ~ +0.4 eV. Almost flat conduction band alignment was realized at x = 0.4 ~ 0.5. On the other hand, at the interfaces over the Ga-rich CIGS, CBM of CIGS was higher than that of CdS, and CBO became negative. The present study reveals that the decrease of CBO with a rise of x presents over the wide rage of x, which results in the sign change of CBO around 0.4 ~ 0.45. In the Ga-rich interfaces, the minimum of band gap energy, which corresponded to energy spacing between CBM of CdS and valence band maximum of CIGS, was almost identical against the change of band gap energy of CIGS. Additionally, local accumulation of oxygen related impurities was observed at the Ga-rich samples, which might cause the local rise of band edges in central region of the interface.