A one-year series of hourly average PM10 observations, which was obtained from the urban and national park air monitoring station at Taipei (Taiwan), was analyzed by descriptive statistics and fractal methods to examine the temporal structures of PM10 concentrations. It was found that all PM10 measurements exhibited the characteristic right-skewed unimodal frequency distribution and long-term memory. A monodimensional fractal analysis was performed by transferring the PM10 concentration time series into a useful compact form: the box-dimension (DB)-threshold (Th) and critical scale (CS)-threshold (Th) plots. Scale invariance was found in these time series and the box dimension was shown to be a decreasing function of the threshold PM10 level, implying multifractal characteristics, (i.e., the weak and intense regions scale differently). To test this hypothesis, the PM10 concentration time series were transferred into multifractal spectra, i.e., the τ(q)-q plots. The analysis confirmed the existence of multifractal characteristics. A simple two-scale Cantor set with unequal scales and weights was then used to fit the calculated τ(q)-q plots. This model fits well with the entire spectrum of scaling exponents for the examined PM10 time series. The relationship between the fractal parameters and classical statistical characteristics, as well as some problems concerning the applicability of fractal methods on air pollution, are discussed.