β-decay half-lives of some magic and semi-magic nuclei have been studied in a fully self-consistent Skyrme Hartree-Fock(HF)plus charge-exchange random phase approximation(RPA).The self-consistency is ad-dressed,in that the same Skyrme energy density functional is adopted in the calculation of ground states and Gamow-Teller excited states.First,the impact of J2 terms on the β-decay half-lives is investigated by using the SGII interaction,revealing a large influence.Subsequently,numerical calculations are performed for the selected nuclei with Skyrme energy density functionals SGII,LNS,SKX,and SAMi.Finally,comparisons to available exper-imental data and predictions of different theoretical models are discussed.