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For single-phase LCL-filtered grid-connected inverter, several control strategies are often used for its better performance, such as active damping for resonance suppression caused by the LCL filter, grid voltage feedforward for high quality of the output current and phase-locked loop (PLL) for grid synchronization. But these control strategies often require additional sensors, which can result in higher cost and unreliability of the whole system. At present, there are some control strategies to reduce the number of sensors, but usually two or more sensors are still needed. In this paper, a control strategy of single-sensor inverter based on full-order state observer is proposed. By sampling the inverter-side current, other state-space variables including the grid voltage and the grid current can be estimated with high accuracy. The simulation results prove that the proposed method performs well with very small observation error, and the control strategy can be easily imposed to maintain the good stability.