Due to high performance demands of grid-connected pulse-width modulation (PWM) converters in power applications, backstepping control (BSC) has drawn wide research interest for its advantages, including high robustness against parametric variations and external disturbances. In order to guarantee these advantages while providing high static and dynamic responses, in this work, a robust BSC (RBSC) with consideration of grid-connected PWM converter parameter uncertainties is proposed for three-phase grid-connected four-leg voltage source rectifiers (GC-FLVSR). The proposed RBSC for GC-FLVSR is composed of four independent controllers based on the Lyabonov theory that control DC bus voltage and input currents simultaneously. As a result, unit power factor, stable DC-bus voltage, sinusoidal four-leg rectifier input currents with lower harmonics and zero-sequence (ZS), and natural currents can be accurately achieved. Furthermore, the stability and robustness against load, DC capacitor, and filter inductance variations can be tested. The effectiveness and superiority of the proposed RBSC compared to the PI control (PIC) have been validated by processor-inthe- loop (PIL) co-simulation using the STM32F407 discovery-development-board as an experimental study.