Aiming at the shortcomings of the correction factor, the paper adjusts the multifractal volatility measure. The model family for HAR with typical feature including jumps, leverage effect, etc., is set up, based on the center for modified multifractal volatility measure. By virtue of empirical analysis of high frequency data from Shanghai composite index, HAR-L-lnMFV$_{t}$-CJ model is the optimal volatility model, according to evaluation criterion: Model goodness of fit, model forecasting and prediction of Value at Risk and this model outperforms traditional model: EGARCH-J and NGARCH-J. All of these studies illustrate that the modified multifractal volatility is a more effective volatility estimator.