We propose a non-linear model predictive scheme for planning fuel efficient maneuvers of small spacecrafts that shall rendezvous space debris. The paper addresses the specific issues of potential limited on-board computational capabilities and low-thrust actuators in the chasing spacecraft, and solves them by using a novel MatLab-based toolbox for real-time non-linear model predictive control (MPC) called MATMPC. This tool computes the MPC rendezvous maneuvering solution in a numerically efficient way, and this allows to greatly extend the prediction horizon length. This implies that the overall MPC scheme can compute solutions that account for the long time-scales that usually characterize the low-thrust rendezvous maneuvers. The so-developed controller is then tested in a realistic scenario that includes all the near-Earth environmental disturbances. We thus show, through numerical simulations, that this MPC method can successfully be used to perform a fuel-efficient rendezvous maneuver with an uncontrolled object, plus evaluate performance indexes such as mission duration, fuel consumption, and robustness against sensor and process noises.