High-speed parallel manipulators are characterized by fast sampling rates and challenges owing to the presence of constraints, high nonlinearities, uncertainties, and fast dynamics. The development of a reliable nonlinear model predictive control (NMPC) approach for this type of robotic systems is challenging because of the complex dynamics that involves high computational burden. To address this control problem, this paper proposes a new fast NMPC strategy applied to high-speed parallel robots. Based on (i) a parameterization technique, (ii) a fast gradient solver, (iii) a proportional integral derivative (PID) control term, (iv) a nonlinear dynamic model, and (v) an artificial neural network (ANN) model, two fast NMPC frameworks were developed to reduce the computational cost of the classical NMPC and address online implementation. In this study, we focus on improving the performance of the standard predictive control strategy outside of the range of its classical applicability by developing a fast NMPC controller for high-speed parallel kinematic manipulators (PKMs). Numerical simulations and real-time experimental results were presented and discussed to validate the relevance of the proposed controllers. Experiments were conducted on a four-degree-of-freedom (4-DOF) PKM called VELOCE developed in our laboratory. The results show that the proposed solution outperforms the original scheme in terms of real-time tracking performance.