Abstract: High-frequency link matrix converter (HFLMC) is getting much concern due to its high efficiency, compact volume and high reliability in the applications, such as vehicle to grid (V2G), energy storage and microgrid. However, under unbalanced grid voltage conditions, HFLMC not only induces current distortion on the grid side which reduces power quality, but also induces double grid-frequency ripples on the dc side, which reduces load and system reliability. To solve the above problems, this paper proposed a nonlinear backstepping control strategy for HFLMC under unbalanced and balanced grid conditions (UBG-BSC). Firstly, the mathematical model of HFLMC was established, and the instantaneous power under unbalanced conditions was analyzed to derive the current reference value in two-phase stationary frame. Then the α backstepping controller and β backstepping controller were designed to track the current reference based on HFLMC mathematical mode. And the stability of HFLMC closed-loop system was proved according to the Lyapunov stability theory. Finally, a 2kW experimental prototype was built. The experimental results show that compared with the traditional PR control strategies, the grid side THD of the proposed UBG-BSC strategy in this paper is reduced by 1.7%, and the ripples on the dc side is reduced by 76%, and the output current response rate is improved by 85%.