The proton and neutron 1S0 pairing gaps and their isospin dependence in isospin asymmetric nuclear matter have been studied by the isospin dependent Brueckner-Hartree-Fock approach and the BCS theory. We have focused on investigating and discussing the effect of three-body force. The calculated results indicate that as the isospin asymmetry increases，the density range of the 1S0 neutron superfluidity is narrowed slightly and the maximum value of the neutron pairing gap increases，while the density domain for the proton superfluidity enlarges rapidly and the peak value of the proton gap decreases remarkably. The three-body force turns out to affect only weakly the neutron 1S0 superfluidity and its isospin dependence，i.e.，it leads to a small reduction of the neutron 1S0 paring gap. However, the three-body force not only reduces largely the strength of the proton 1S0 gaps at high densities in highly asymmetric nuclear matter but also suppresses strongly the density domain for the proton 1S0 superfluidity phase.