We have measured the Z-boson production differential cross section as a function of transverse momentum using Z\ensuremath{\rightarrow}ee and Z\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\mu} decays in p\ifmmode\bar\else\textasciimacron\fi{}p collision at \ensuremath{\surd}s =1.8 TeV with the Collider Detector at Fermilab. Comparison with standard-model predictions shows good agreement over the range 0${\mathit{p}}_{\mathit{T}}$160 GeV/c available from this data sample.