Currently, the types for fault diagnosis of three-phase inverters are mostly linear loads. As nonlinear loads are more and more widely used, the original methods make it difficult to solve the harmonic problems caused by nonlinear loads during faults. In addition, the existing fault diagnosis methods are mostly for switches or sensors, without comprehensive consideration of the above faults. To address the aforementioned problems, a simultaneous diagnostic method for open-circuit faults and current sensor faults in two-level three-phase inverters with nonlinear loads is proposed in this article. The inverter three-phase current state-space equation is formulated and the actual duty cycle function is derived. The continuous duty cycle function is used instead of the discrete switching function. Therefore, the state-space equation meets the observation requirements. A discrete sliding mode observer based on composite control is designed. It adopts the structure of zero-phase-shift repetitive control and proportional integral control in series, which can effectively track the harmonic current. Adjustable factor detection variables and adaptive thresholds are designed. The fast and accurate fault diagnosis can be realized by adjusting the adjustment factors. A test bench is established and experimentally evaluated that the diagnosis time for open-circuit faults is less than 3 ms, and the diagnosis time for sensor faults is less than 6 ms. The proposed fault diagnosis method can realize fast diagnosis of both open-circuit faults and sensor faults under nonlinear loads.