The control of high-speed AC/DC-converters is still a very demanding task. This paper presents an online optimizing nonlinear model predictive control (MPC) strategy, which allows to reach long prediction horizons in the range of 100 times the sampling time. The MPC is complemented by estimation strategies for the grid phase voltages and the load current. To achieve a short calculation time of the MPC in the range of a few μs, the MPC is tailored to the efficient implementation on an FPGA. This is achieved by using the parallel computation capabilities of FPGAs and pipelining methods, and by avoiding time-and resource-demanding operations like trigonometric functions. Compared to other MPC methods discussed in the literature, the proposed MPC strategy allows for significantly longer prediction horizons. The performance and the robustness of the control strategy is evaluated by measurements on a hardware-in-the-loop test bench.