This paper has collected all available optical B magnitudes of quasar 3C345 of more than 100 years, and acquired it's long-term light curve. We make a muti-time scale analysis to it's B band data with the wavelet analysis method, and get the wavelet transform coefficient plots to demonstrate the explosion process of the optical B band of 3C345. From the analysis, we have found that threr exist approximate periods of 450 d, 780 d, 1830 d and 3540 d. The inverse wavelet transform shows the light curve variability of 3C345 on different time scales, so we can predict it's possible explosion time is the year of 2010.