A search for highly ionising, penetrating particles with electric charges from |q| = 2e to 6e is performed using the ATLAS detector at the CERN Large Hadron Collider. Proton-proton collision data taken at sqrt(s)=7 TeV during the 2011 running period, corresponding to an integrated luminosity of 4.4 fb^-1, are analysed. No signal candidates are observed, and 95% confidence level cross-section upper limits are interpreted as mass-exclusion lower limits for a simplified Drell--Yan production model. In this model, masses are excluded from 50 GeV up to 430, 480, 490, 470 and 420 GeV for charges 2e, 3e, 4e, 5e and 6e, respectively.