Quantile regression allows one to predict the volatility of time series without assuming an explicit form for the underlying distribution. Financial assets are known to have irregular return patterns; not only the volatility but also the distribution functions themselves may vary with time, so traditional time series models are often unreliable. This study presents a new approach to volatility forecasting by quantile regression utilizing a uniformly spaced series of estimated quantiles. The proposed method provides much more complete information on the underlying distribution, without recourse to an assumed functional form. Based on an empirical study of seven stock indices, using 16 years of daily return data, the proposed approach produces better volatility forecasts for six of the seven indices.