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We study the seemingly duality between large and small $\eta_H$ for theconstant-roll inflation with the second slow-roll parameter $\eta_H$ being aconstant. In the previous studies, only the constant-roll inflationary modelswith small $\eta_H$ are found to be consistent with the observations. Theseemingly duality suggests that the constant-roll inflationary models withlarge $\eta_H$ may be also consistent with the observations. We find that theduality between the constant-roll inflation with large and small $\eta_H$ doesnot exist because both the background and scalar perturbation evolutions arevery different. By fitting the constant-roll inflationary models to theobservations, we get $-0.016\le\eta_H\le-0.0078$ at the 95\% C.L if we take$N=60$ for the models with increasing $\epsilon_H$ in which inflation ends when$\epsilon_H=1$, and $3.0135\le \eta_H\le 3.021$ at the 68\% C.L., and$3.0115\le \eta_H\le 3.024$ at the 95\% C.L. for the models with decreasing$\epsilon_H$.

On the constant-roll inflation with large and small $\eta_H$