We study cosmological dynamics of the constant-roll inflation with a hilltop potential, where the potential has a very small deviation from the exactly flat one. After presenting the main equations of the inflation phase, we express the scalar spectral index and tensor-to-scalar ratio in terms of the e-folds number and the mentioned deviation parameter. By performing some numerical analysis on the model parameters space and comparing the results with Planck2018 TT, TE, EE+lowE+lensing+BAO+BK14 data, we find some constraints on the deviation parameter at both 68 and 95% CL. We show that in the constant-roll inflation with hilltop potential, there is no instantaneous reheating and few e-folds are needed for reheating process to be completed.
