A measurement of the multi-strange Ξ- and Ω- baryons and their antiparticles by the ALICE experiment at the CERN Large Hadron Collider (LHC) is presented for inelastic proton-proton collisions at a centre-of-mass energy of 7 TeV. The transverse momentum (pT) distributions were studied at mid-rapidity (|y|<0.5) in the range of 0.6<pT<8.5 GeV/c for Ξ- and Ξ-+ baryons, and in the range of 0.8<pT<5 GeV/c for Ω- and Ω-+. Baryons and antibaryons were measured as separate particles and we find that the baryon to antibaryon ratio of both particle species is consistent with unity over the entire range of the measurement. The statistical precision of the current data has allowed us to measure a difference between the mean pT of Ξ- (Ξ-+) and Ω- (Ω-+). Particle yields, mean pT, and the spectra in the intermediate pT range are not well described by the PYTHIA Perugia 2011 tune Monte Carlo event generator, which has been tuned to reproduce the early LHC data. The discrepancy is largest for Ω- (Ω-+). This PYTHIA tune approaches the pT spectra of Ξ- and Ξ-+ baryons below pT<0.85 GeV/c and describes the Ξ- and Ξ-+ spectra above pT>6.0 GeV/c. We also illustrate the difference between the experimental data and model by comparing the corresponding ratios of (Ω-+Ω-+)/(Ξ-+Ξ-+) as a function of transverse mass. © 2012 CERN.