We have investigated the renormalization group running of the pole mass in the multi-Higgs theory in two different types of the gauge fixing conditions. It turns out that the pole mass when expressed in terms of the Lagrangian parameters, is invariant under the renormalization group with the beta and gamma functions of the symmetric phase.The pole mass plays an important role in the process where the characteristic scale is close to the mass shell [1] and was shown to be infrared finite and gauge invariant [2]. The physical quantities such as the pole mass and the beta functions obtained in the minimal subtraction(MS) scheme was used in determining the Higgs mass bound [3] or the vacuum stability analysis[4]. These beta functions take different forms when calculated in different renormalization schemes [5] and in most of the cases, they are obtained in the symmetric phase with the MS scheme[6] and the pole masses we are interested in are those in the broken symmetry phase. Hence, it seems to be necessary to investigate the renormalization group(RG) behavior of the physical quantities such as the pole mass in the broken phase under the beta functions in the symmetric phase and it was shown that if the pole mass was expressed in terms of the Lagrangian parameters in the symmetric phase it is RG invariant under the beta and gamma functions obtained in the symmetric phase in the minimal subtractions(MS) scheme in case of the neutral scalar and the Abelian Higgs model [7][8] and also have shown the gauge parameter independence [9]. Recently, the models with non-minimal Higgs bosons are of interest in the new physics to solve the question of the origin of the neutrino mass, matter-antimatter asymmetry in the universe and the nature of dark matters[10] and in this paper, we will investigate the RG behavior of the Higgs pole mass in these multi-Higgs model by generalizing the method that we have used in [7][8].The pole masses M 2 i of the multi-Higgs model is determined as [11] det Ξ pq (p 2 ) p 2 =βM 2 i