In the current paper, the characteristic factor β=[1 +0.904(σb / σs) · (1-σs / σb)] is extracted from the analytical solution of the bending moment for a rectangular strainhardening beam first. Thereafter, the characteristic factor β is transplanted into the previously proposed assessment of the critical buckling strain for rigid-perfectly plastic bending pipe by analogy method, thus an extended expression of the critical buckling strain for a pipe plastic bending including strain-hardening effect is developed, εc=0.19tr⋅(1+11.78r)⋅[0.096+0.904/(1−n)2].εc=0.19tr⋅(1+11.78r)⋅[0.096+0.904/(1−n)2]. Moreover, available test data is employed to check the suitability of the extended expression. The results show that the extended expression is reasonable to reveal the effect of Hollomon type strain-hardening behavior on the critical buckling strain of pipe plastic bending.