This paper presents a sliding-mode control (SMC) strategy for single-phase grid-connected LCL-filtered voltage source inverters (VSIs) with double-band hysteresis scheme. The proposed SMC is simpler than the existing SMC methods devised for grid-connected VSIs since its sliding-surface function requires the sensing of capacitor voltage and grid current only. In addition, a double-band hysteresis scheme which ensures the switching of a transistor in the VSI during a half cycle while it remains either on or off in the other half cycle of the fundamental period is used to mitigate the switching frequency. Furthermore, the analytical expressions for the instantaneous and average switching frequencies are derived. The theoretical considerations and analytical results are verified through computer simulations and experimental results obtained from a 3.3-kW system. Simulation and experimental results show that the proposed SMC strategy exhibits an excellent performance in achieving the required control objectives such as fast dynamic response, robustness, sinusoidal grid current with low total harmonic distortion, and simplicity in a practical implementation.