To describe the stylized features of volatility comprehensively, this paper embeds the time-varying leverage effect of volatility into the Realized Generalized AutoRegressive Conditional Heteroskedasticity (RG) model and proposes a new volatility model with a time-varying leverage effect. The Quasi-Maximum Likelihood-Kernel (QML-K) method is proposed to approximate the density function of returns and to estimate the parameters in the new model. Under some mild regularity conditions, the asymptotic properties of the resulting estimators are achieved. Simulation studies demonstrate that the proposed model yields better performances than traditional RG models under different situations. Finally, the empirical analysis shows better finite sample performance of the estimation method and the new model on real data compared with existing methods.