We investigate a striking example of mirror asymmetry in Gamow-Teller (GT) βdecay using the nuclear shell-model including isospin-nonconserving (INC) forces in the sd-shell region. We show that the large mirror asymmetry between 26 P and 26 Na GT β-decay can be accurately reproduced by introducing T = 1, J ̸ = 0 INC forces related to the s 1/2 orbit, while the usual J = 0 INC force, commonly adopted to describe isospin-symmetry breaking, does not work. We further show that the calculated distribution of summed GT strength for the 26 P β-decay is in good agreement with the experimental data. Our results support the conclusion that 26 P is a nucleus with proton-halo structure.