The Cantor set fractal distribution and probability model are combined to analyze earthquake time series of two seismogenic zones of Taiwan from 1900 to 1999. One-dimensional box counting method is adopted to measure the occurrence probability of earthquakes equal to or larger than a certain magnitude threshold with different time scales. The results show that the fractal dimension has a negative correlation with the magnitude threshold, and the ideal critical time scale has an exponential correlation with the magnitude threshold. The ideal critical time scale can be deemed as the "lower limit" of recurrence period of earthquake clustering that can be referenced in designing earthquakes occurred in the Chianan zone, we suggest that the fault activities in the Chianan zone are more active than that in the Center zone of Taiwan.