Widely used volatility forecasting methods are usually based on low frequency time series models. Although some of them employ high frequency observations, these intraday data are often summarized into a point low frequency statistic, e.g., a daily realized measure, before being incorporated into a forecasting model. This paper contributes to the volatility forecasting literature by instead predicting the next-period intraday volatility curve via a functional time series forecasting approach. In contrast with non-functional methods, the proposed functional approach fully exploits the rich intraday information and hence leads to more accurate volatility forecasts. This is further confrmed by extensive comparisons between the proposed functional method and those widely used non-functional methods in out-of-sample volatility forecasting for a number of stocks and equity indices from the Chinese market.