Based　on　the　numerical　method　proposed　in　Hu　et　al.　(2018)　[22]　for　Kohn-Sham　equation,　further　improvement　on　the　efficiency　is　obtained　in　this　paper　by　i).　designing　a　numerical　method　with　the　strategy　of　separately　handling　the　nonlinear　Hartree　potential　and　exchange-correlation　potential,　and　ii).　parallelizing　the　algorithm　in　an　eigenpairwise　approach.　The　feasibility　of　two　approaches　is　analyzed　in　detail,　and　the　new　algorithm　is　described　completely.　Compared　with　previous　results,　a　significant　improvement　of　numerical　efficiency　can　be　observed　from　plenty　of　numerical　experiments,　which　make　the　new　method　more　suitable　for　the　practical　problems.(c)　2022　Elsevier　Inc.　All　rights　reserved.