A crystal-plasticity finite-element method was used to examine the deformation mechanism in a commercially pure titanium sheet. The following tension-compression asymmetry was exhibited in the stress-strain curves: the yield stress was larger under tension than under compression, whereas the work-hardening was smaller under tension than under compression. The strain hardening behaviour was predicted qualitatively well using the crystal-plasticity analysis. The simulation results suggested that the tension-compression asymmetry could be explained in terms of the difference in the activity of the twinning systems.