The muon number of cosmic-ray air showers detected by the KASCADE-Grande experiment is presented as a function of the primary energy between $10^{16}$ eV and $10^{18}$ eV for three zenith angle intervals. For this work, data with zenith angles smaller than 40 degrees and radial distances between 150 m and 650 m from the core are used. The measurements correspond to 5 years of effective time of observation. For energy calibration a method based on the comparison of the measured muon-number distributions with the respective Monte Carlo (MC) predictions from the GSF model and the Pierre Auger energy scale is employed. For this procedure, we used the hadronic-interaction models QGSJET-II-04, EPOS-LHC and SIBYLL 2.3d. The results are compared with the corresponding MC estimations for the GSF model and for pure protons and iron nuclei. We found that while for larger shower inclinations, one observes a reasonable agreement between the simulation results and the data of KASCADE-Grande, current interaction models tend to overestimate the muon number in vertical air showers.