The radio fluxes of the quasars 3C 345, 3C 279 and 3C 273 at a frequency of 8.0 GHz were collected in a time period from 1965 to 2012 based on the database of University of Michigan Radio Astronomy Observatory. The time series of the quasar variability is decomposed into trend components, periodic components and high frequency components by the ensemble empirical mode decomposition. Then chaotic characteristic quantities of the high frequency component is analyzed, that is, saturation correlation dimension, maximum Lyapunov exponent and Kolmogorov entropy. The results show that the variability of quasars has the chaotic characteristic as well as the characteristic of periodicity. The variability of quasars is due to the comprehensive consequence of a physical mechanism of the periodic phenomenon combined with the nonlinear mechanism of the chaos phenomenon.