The three-level direct matrix converter (TLDMC) has attracted wide attention in the fields of motor drive, distributed power generation, and renewable energy because of its advantages of high power density, high efficiency, and low common mode voltage. However, in unbalanced grid voltage conditions, the current distortion on the input side of the TLDMC will affect the power factor and power quality of the output side, and reduce the reliability of the system. The existing TLDMC input closed-loop control strategy cannot meet the requirements of high dynamic response and robustness. To this end, a TLDMC nonlinear control strategy is proposed based on back-stepping sliding-mode control (BS-SMC) which is suitable for balanced and unbalanced grid voltage conditions without positive and negative sequence separation. A dynamic modulation index is used to suppress the ripple of the active power double frequency in unbalanced conditions. The input reactive power is controlled by eliminating the nonlinear term in the Lyapunov derivative function and applying a sliding mode surface as a virtual error. After theoretical analysis and comparative experiments, the results show that compared with the traditional control strategies, the response speed of the back-stepping sliding-mode control is increased, and the THD is reduced. The method proposed provides a reference for the input control strategy of matrix converters.