A non-linear reduced-order state observer was designed and a system control method based on the observer was proposed, in order to achieve capacitive voltage balance among modules of the modular multilevel converter (MMC) and reduce the number of voltage sensors. According to the three-phase MMC topology, a state-space model was established with three-phase circulating current, alternating output currents and capacitive voltages of all modules as state variables. Combining the model, an observer design method was proposed. The observer measured six bridge arm currents and six bridge voltages in the MMC circuit, and combined switching signals to obtain capacitance voltage of each module. Using the passivity theory and the persistently and sufficiently exciting condition, it is proved that the observer error model is uniformly asymptotically stable under the carrier phase shift modulation strategy and the nearest level modulation strategy. A MMC power and current double closed-loop controller was designed based on the observer. Simulations show that the observed values of the designed observer can accurately track the actual values, and the system has good robustness and dynamic performance.