Rate-independent crystal plasticity model suffers from the non-uniqueness of activated slip systems and the determination of the shear slip rates on the active slip systems. In this paper, a time-integration algorithm which circumvents the problem of the multiplicity of the slip systems was developed and implemented into the user subroutine VUMAT of a commercial finite element program ABAQUS. The magnitude of the slip shears on the active slip systems in f.c.c Cu single crystal aligned with the specific crystallographic orientation was investigated to validate our solution procedure. Also, texture developments under various deformation modes such as simple compression, simple tension and plane strain compression were compared with the results of the rate-dependent model by using the rate-independent crystal plasticity model. The computation time employing the rate-independent model is much more reduced than the those of the rate-dependent model.