We compute renormalized vertices of the 125 GeV Higgs boson h with the weak gauge bosons (hVV), fermions (hff), and itself (hhh) in the Georgi-Machacek model at one-loop level. The renormalization is performed based on the on-shell scheme with the use of the MS scheme only for the hhh vertex. We explicitly show the gauge dependence in the counterterms of the scalar mixing parameters in the general R ξ gauge and that the dependence can be removed by using the pinch technique in physical scattering processes. We then discuss the possible allowed deviations in these one-loop corrected Higgs couplings from the standard model predictions by scanning model parameters under the constraints of perturbative unitarity and vacuum stability as well as those from experimental data.