The neutron 3PF2 pairing gap in pure neutron matter has been studied by using the Brueckner-Hartree-Fock(BHF) approach and the BCS theory. We have concentrated our attention on investigating the three-body force effect on the neutron superfluidity in the 3PF2 channel. The calculated results indicate that the three-body force enhances remarkably the 3PF2 superfluidity in neutron matter. When adopting the BHF single-particle spectrum, the three-body force turns out to increase the maximum value of the pairing gap from about 0.22MeV to about 0.5MeV.