In this paper, a generalized extended state observer (GESO) is proposed to accurately observe supercapacitor's state of charge (SOC) by counteracting the modeling deviation and disturbances. With the consideration of dynamic modeling uncertainty and disturbances, a nonlinear mathematical model is established based on the three branch equivalent circuit model for supercapacitor (SC). A GESO is designed to observe SC's internal capacitance voltage and modeling error with the known information from the established mathematical model. With the estimated modeling error information, a compensation control law is designed to eliminate deviation, which results in an accurate internal capacitance voltage observation. An accurate SOC for SC is obtained with the estimated parameters. Experimental results from a synchronous buck circuit based test platform are provided to verify the feasibility and superiority for SOC observation by GESO.