Cu(In,Ga)3Se5 (β-CIGS) has a band gap of 1.35 eV, which is an optimum value for high solar-energy conversion efficiency. The effects of Cu and Ga content on the cell performance were investigated previously. However, the effect of Se content on the cell performance is not well understood yet. In this work, β-CIGS films were fabricated by three-stage co-evaporation of elemental sources with various Se fluxes at the third stage instead of at all stages. The average composition of five samples was Cu1.05(In0.59,Ga0.41)3Sey, where the stoichiometric y value is 5.03 and the stoichiometric Se/metal (Se/M) ratio is 1.24. We varied the Se/metal ratio in a range from 1.18 to 1.28. We found that the best efficiency was achieved when the Se/M ratio was 1.24, which is exactly the stoichiometric value where the CIGS grains on the CIGS surface were tightly connected and faceted. With the optimum Se/M ratio, we were able to enhance the cell efficiency of a β-CIGS solar cell from 9.6% to 12.0% by employing a Na2S post deposition treatment. Our results indicate that Na2S post deposition treatment is very effective to enhance the cell efficiency to a level on par with that in α-CIGS cell.