The low-lying states of the mid-heavy odd-even Sb-111 and odd-odd Sb-112 isotopes are calculated for the first time within the shell model framework. The shell model calculations have been carried out within the reduced model space including the single particle orbits 1d(5/2), 0g(7/2), 1d(3/2), 2s(1/2). We obtain the energy spectra for the Sb-111 and Sb-112 isotopes in the reduced model space by using CD-Bonn two-body effective nucleon-nucleon interaction. The energy spectra are compared to the experimental results to give some discussion about the low-lying states of Sb-111 and Sb-112.