In this study, the local texture evolution during high pressure torsion (HPT) deformation of aluminum single crystal is predicted by the crystal plasticity finite element method model integrating crystal plasticity constitutive theory with the Bassani and Wu hardening law. It has been found the lattice rotates mainly around the sample radial direction to accommodate the increasingly introduced plastic strain. A noticeable amount of lattice rotation angles around the axial direction have also been observed at a certain HPT stage. The crystallographic orientation changes as the lattice rotates. With increasing HPT deformation, the initial cube orientation rotates progressively to the rotated cube orientation, then to the C component of ideal torsion texture which could be maintained over a wide strain range, and further HPT deformation leads the orientation towards the ideal component.The HPT induced orientation changes and lattice rotations have been discussed in detail based on the theory of crystal plasticity.