In this study, we present a ground-motion model for the vertical component of peak ground acceleration, peak ground velocity, and 5% damped pseudo acceleration response spectra at periods ranging from 0.01 to 4 s. The vertical model is based on the ground-motion models previously developed for the horizontal component and vertical-to-horizontal ratio of ground motion by Akkar et al. (Bull Earthq Eng 12:359-387, 2014a; 517-547, 2014b) rather than on an independent regression analysis of strong-motion data available for Europe and the Middle East. The proposed ground-motion model includes formulations for the median values as well as for the aleatory within-event, between-event, and total standard deviation values of the vertical ground motion. We validate the proposed model by comparing it against the strong-motion database of Europe and the Middle East. Our vertical ground-motion model is applicable for moment magnitudes ranging from 4.0 to 8.0, for source-to-site distances ranging from 0 to 200 km, average shear-velocity down to 30 m (V-s30) values ranging from 150 to 1200 m/s and for reverse, normal and strike-slip styles of faulting as is the case for the underlying horizontal component and vertical-tohorizontal ratio ground-motion models of Akkar et al. (2014a, b). Within the scope of this study, a method to develop a vertical spectrum that is fully consistent with the corresponding horizontal uniform hazard spectrum is also proposed.