A novel gap-filling method called the diurnal-cycle-constrained empirical orthogonal function (DCCEOF) is proposed. Cross validation indicates that this method gives high accuracy in predicting missing values in daily PM_2.5 time series by accounting for the local diurnal phases, especially by reconstructing daily extrema that cannot be accurately restored by other approaches. The DCCEOF method can be easily applied to other data sets because of its self-consistent capability.