Higgs potential, which spoil predictive power of the model. Hence, it is important to clarify allowed regions in the parameter space not only by using current experimental data but also by investigating theoretical consistencies such as perturbative unitarity [@Lee:1977yc; @Dicus:1992vj], vacuum stability and triviality [@Lindner:1985uk]. This kind of study has been often developed to constrain parameters of the Higgs sector in the context of the two-Higgs-doublet model [@Kanemura:1993hm; @Ginzburg:2005dt; @Komatsu:1981xh; @Nie:1998yn], and in a specific triplet model [@Forshaw:2003kh].

In this paper, we study bounds on Higgs boson masses from perturbative unitarity in the Georgi-Machacek (GM) model. The Higgs potential respects the global $SU(2)_R$ symmetry, so that the custodial $SU(2)_{\rm V}$ symmetry remains after the electroweak symmetry breaking ($SU(2)_{L} \otimes SU(2)_R \to SU(2)_{\rm V}$). There are ten physical scalar states, which can be expressed by a $SU(2)_{\rm V}$ 5-plet $(H_5^{++}, H_5^+, H_5^0, H_5^-, H_5^{--})$, a 3-plet $(H_3^+, H_3^0, H_3^-)$ and two singlets $\tilde{H}_1^0$ and $\tilde{H}^{0'}_{1}$ [@Georgi:1985nv]. The scalar components in the same multiplet are degenerate in mass at the tree level. In the Higgs potential of the GM model, explicit $Z_2$ violation can only appear in the trilinear scalar interaction, but they must be forbidden to avoid excessive magnitudes for masses 