In this paper

the chaotic condition and chaotic root of the earthquake precursor observation time series are discussed

and the problem of how to recognize anomalous element of the earthquake precursor observation time series is studied from the point of view of wavelet transform with multi-scale analysis combining with fractal theory according to good localized characteristic of time and frequency of wavelet transform and the variation characteristic in fractal dimension. It is indicated that the variation of fractal dimension of time series′ wavelet transform coefficient with scale shows smoothly and slowly reductive variation in most of time intervals.In anomalous time intervals

the peculiarity of the variation curves shows the instance of peak value

in which the curve varies from high value to low value first and then varies from low value to a relatively high value and then it slowly reduces at a peak value.The anomalous information is checked out two months to one year before the earthquakes in the examples.To study earthquake problem by combining wavelet theory with fractal theory is not only the exploitation for a new field of earthquake research

but also the continuation for the application of wavelet transform and fractal theory.