Currently, the load types for fault diagnosis of three-phase inverters are mostly linear loads, and as nonlinear loads are more and more widely used, the original methods are 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 solve the above 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 paper. The inverter three-phase current state-space equation is established and the actual duty cycle function is derived, and the continuous duty cycle function is used instead of the discrete switching function, so that the state-space equation meets the observation requirements. A discrete sliding mode observer based on composite control is designed. The composite control 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, and fast and accurate fault diagnosis can be realized by adjusting the adjustment factors. A test bench is built and experimentally verified 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.