Stock index futures plays an important role in the process of price discovery and risk prevention of capital market. The prediction of its return volatility is significantly important to achieve the risk aversion function of stock index futures. A semiparametric forecasting model based on the linear nonnegative autoregressive model is proposed to forecast the realized volatility of stock index futures, and the asymptotic properties of estimation method for this model are analyzed. In addition, taking 5 min highfrequency trading data of CSI300 index futures as example, the outofsample daily volatility predictions calculated by using rolling predicting method, and a bootstrap MCS test is used to evaluate the predicting accuracy for the proposed model and other 7 models. The empirical results show that, under various robust loss functions, the proposed model is the best model for volatility predictions of stock index futures among the 8 models.