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Using a new phenomenological (K)N interaction which reproduces A(1405) as an I = 0 bound state of (K)N, we have investigated K- -3 He(T = 0) and K- -4 He(T = 1/2) within the framework of the Brueckner-Hartree-Fock(BHF) theory. Our calculations show that the above kaonic nuclear systems are both deeply bound. The binding energy BK- is 124.4 MeV(94.1 MeV) and the width Γ is 11.8 MeV(25.8 MeV) for K- -3 He(T = 0)(K- -4 He(T= 1/2)).