Crystal plasticity theory is a well-established and powerful framework for analyzing plasticity at different scales. Constitutive models incorporate crystallographic slip systems and are formulated by multisurface yield criterions based on Schmid’s law. Unfortunately, rate-independent crystal plasticity models face long-standing problems regarding the determination of active slip systems and the unique computation of plastic slips on those systems. Although, rate-dependent models might regularize the problem through a viscous formulation, these models face the same problems when approaching their rate-independent limit. Therefore, many algorithms have been proposed in the literature which pose additional constitutive assumptions on the level of the linear system of equations by a numerical manipulation. Recently, the idea of utilizing the benefits of constraint optimization, in particular, interior-point methods was advocated in [1]. Based thereon, we develop a new return map interior-point algorithm for finite-strain rate-independent crystal plasticity [2]. The algorithm is consistently derived from the postulate of maximum dissipation while utilizing several techniques known from interior-point schemes. Furthermore, algorithmic features necessary in order to produce a fast and stable algorithm are outlined. Several numerical examples including finite element simulations are presented in order to demonstrate the robustness and efficiency of the algorithmic formulation. Additionally, the results are compared with the well-established augmented Lagrangian formulation.