Event-shape observables measured using charged particles in inclusive Z-boson events are presented, using the electron and muon decay modes of the Z bosons. The measurements are based on an integrated luminosity of [Formula: see text] of proton-proton collisions recorded by the ATLAS detector at the LHC at a centre-of-mass energy [Formula: see text] [Formula: see text]. Charged-particle distributions, excluding the lepton-antilepton pair from the Z-boson decay, are measured in different ranges of transverse momentum of the Z boson. Distributions include multiplicity, scalar sum of transverse momenta, beam thrust, transverse thrust, spherocity, and [Formula: see text]-parameter, which are in particular sensitive to properties of the underlying event at small values of the Z-boson transverse momentum. The measured observables are compared with predictions from Pythia 8, Sherpa, and Herwig 7. Typically, all three Monte Carlo generators provide predictions that are in better agreement with the data at high Z-boson transverse momenta than at low Z-boson transverse momenta, and for the observables that are less sensitive to the number of charged particles in the event.