We present an empirical approach to modelling the vertical (vector) profile of large ocean currents, based on a conditional extremes model (Heffernan and Tawn, 2004) from the statistics literature. Observed vector currents at each of a number of water depths are expressed as components with respect to major- and minor-axis of current variation at that depth using Principal Components Analysis. Each current component is then independently decomposed into the sum of (deterministic periodic) tidal and (random) non-tidal currents using a local harmonic model. The marginal and dependence structure of extremes of hourly maxima and minima of non-tidal components is characterised using the conditional extremes model. We simulate under this model to estimate characteristics of extreme current profiles corresponding to arbitrary return periods, and quantify the uncertainty of those estimates. For a sample collected over a 2.5-year period in 250 m water on the outer shelf of North Western Australia, the model predicts monthly instantaneous extreme conditional profiles well. We also estimate marginal and conditional current profiles corresponding to a 10-year return period. © 2011 Elsevier Ltd.