Considering a reduced center-of-mass model for bipedal walking, by utilizing the Capture Point as a system coordinate one can separate the stable and unstable components of the dynamics. In this paper, previous works on the stabilization of the Capture Point dynamics are extended by employing model predictive control (MPC). This allows to explicitly incorporate constraints on the zero-moment-point (ZMP) in the controller design. The proposed Capture-Point-MPC is evaluated in simulation and experiments with the DLR-Biped.