In the framework of GARCH models，Li et al. (2015) proposed a new hyperbolic GARCH model (denoted by HGARCH) ，which can parameterize both long memory decay and dramatic amplitude of volatilities as the HY-GARCH model (Davidson，2004) . What’s more，the non-negative restrictions on the parameters in the HGARCH model are more tractable than those counterparts in HY-GARCH models. However，it is well known that when the time series covers a long time span，a constant structure is usually inadequate to capture possible structure changes. To address this issue，this paper constructs a new dynamic mixture hyperbolic GARCH (denoted by DM-HGARCH) model. The DM-HGARCH model accommodates covariance stationarity，long memory and structural changes in volatilities simultaneously. Conditions for the existence of weak stationary solutions are investigated and the EM algorithm is employed for parameter estimation. MonteCarlo simulations are conducted to evaluate the finite-sample performance. Finally，the new model is applied to the daily log returns of Shanghai stock exchange( SSE) index in China and S&P 500 index in USA respectively. The empirical study illustrates that in the given sample period，the DM-HGARCH performs better on the latter index than the former one in terms of both in-sample fitting and out-of-sample forecasting.