Power converters and control strategies are very vital for the increasing sustainability of the power grid targeting smart grids. In these circumstances, it is proposed a novel single-phase five-level (SP5L) VIENNA rectifier digitally controlled by a model predictive control (MPC) with fixed switching frequency, which can be useful for a variety of applications with a robust current tracking. The proposed SP5L VIENNA rectifier is an advancement of the classical three-level VIENNA rectifier, also contributing to preserve power quality, and exhibiting the advantage of operating with more voltage levels at the expense of few additional switching devices. The proposed topology is introduced and correlated with the classical solutions of active rectifiers. The operation principle is introduced and used to describe the MPC, which is given in detail, as well as the necessary modulation strategy. The results were obtained for a set of various operating conditions, both in terms of reference of current and grid-side voltage, as well as in steady-state and transient-state, proving the benefits of the proposed SP5L VIENNA rectifier and the accurate and precise use of the MPC to control the grid-side current.