A dislocation density based constitutive model for face-centred cubic crystals is introduced and implemented into a crystal plasticity finite element framework. The approach assumes a homogeneous dislocation structure and tracks the dislocation evolution on each slip system. In addition to the statistically stored dislocations, the geometrically necessary dislocation density is introduced in order to consider strain gradients and thus render the model size sensitive. Furthermore, we develop a consistent algorithm for the updating of the geometrically necessary dislocation density. A simple shear experiment of an aluminium single crystal is used to calibrate the material parameters of the model and demonstrate its size sensitivity.