An explicit integration scheme for rate-dependent crystal plasticity (CP) has been developed in this work. Additive decomposition of the velocity gradient tensor into lattice and plastic parts is adopted for describing the kinematics; the Cauchy stress is calculated by using a hypo-elastic formulation, applying the Jaumann stress rate. This CP scheme has been implemented into a commercial finite element code (CPFEM). Uniaxial compression and rolling processes are simulated. The results showed good accuracy and reliability of the integration scheme. The results were compared to simulations using the hyper-elastic viscoplastic implementation by Dumoulin et al , involving multiplicative decomposition of the deformation gradient tensor. It was found that the hypo-elastic implementation is only slightly faster and has a similar accuracy as the hyper-elastic formulation.