This paper develops a single-crystal plasticity model with Johnson–Cook-type hardening laws to examine the strain rate and temperature sensitivities of magnesium (Mg). Slip, twinning and their interactions are deemed the dominant plastic mechanisms. The twinning-induced lattice reorientation is implemented by taking the initial grain after reorientation as a “new” grain with an updated orientation. Distinct strain rate and temperature dependences are considered for different slip and twinning modes. Non-basal slip is believed strain rate and temperature dependent, while compression twinning (CT) is assumed to exhibit temperature sensitivity in a certain temperature range. To validate the proposed model, plane-strain compression tests of Mg crystals under different strain rates and temperatures are simulated. The experimental data available in the literature are compared with the predicted results, and the tendencies of stress–strain curves are analyzed based on the corresponding evolution of slip and twinning. It is found that twinning-induced lattice reorientation significantly influences the mechanical behavior of Mg, especially when tension twinning (TT) dominates the plastic deformation. High temperatures and low strain rates enhance the activity of non-basal slip, and CT becomes easily activated as the temperature is increased beyond 150∘C, which coincides well with experimental observations. The strain rate sensitivity rising with temperature is also predicted by the model.