This paper presents a current sensorless control strategy for a three-phase multi-level active front-end rectifier with an LCL filter. The proposed control strategy is based on the mathematical model of the system. Opposed to the existing control methods that measure three-phase currents as well as three-phase voltages, the proposed control eliminates the current measurement requirement which leads to cost reduction. Moreover, unlike the existing current control methods that use two proportional-integral (PI) controllers, the proposed current control does not use any PI controller in the current loop. The elimination of two PI controllers simplifies the controller design. The resonance damping requirement arising due to the LCL filter is tackled by active damping that is realized by using filter capacitor voltage feedback. The steady-state and dynamic performances of the proposed control strategy are investigated experimentally under balanced, unbalanced and distorted grid conditions.