A meso-scale numerical constitutive model was established by the theory of crystal plasticity and the finite element method to describe the mechanical behavior of the hexagonal close-packed (hcp) metal. Based on this model, the one-way tensile experiment on a single crystal of titanium at elevated temperature was simulated. The simulated results are consistent with the experimental ones, indicating that the model is reliable. The calculated results also reveal the action of each slip system in deformation process of single crystal titanium. The meso-scale deformation evolution, including grid slipping and crystal lattice reorientation, during the tensile deformation was also analyzed.