This paper proposes a parallelizable real-time algorithm for model predictive control (MPC). In contrast to existing distributed and parallel optimization algorithms for linear MPC such as dual decomposition or the alternating direction method of multipliers (ADMM), the proposed algorithm can deal with nonlinear dynamic systems as well as non-convex stage costs. Existing real-time algorithms for MPC simulate and compute sensitivities of the predicted state trajectories on the whole prediction horizon. Different from this, the proposed method uses a reversed real-time scheme, where small-scale nonlinear MPC problems are solved on much shorter horizons and in parallel during the feedback phase, while a large equality constrained coupled QP is solved during the preparation step. This makes the proposed algorithm particularly suited for nonlinear MPC problems with long prediction horizons. The performance and advantages of the proposed method compared to existing real-time nonlinear MPC algorithms are illustrated by applying the method to a benchmark case study.