The physical mechanism of multiple modes in dynamics of polyelectrolyte aqueous solutions has been drawing extensive research attention for decades. This unsolved mystery makes it highly desirable to use new techniques to conduct investigations. In this study, dual-color fluorescence cross-correlation spectroscopy is applied to study the dynamics of individual molecules of a model polyelectrolyte, sodium poly(styrene sulfonate), in aqueous solutions. Anticorrelation in the cross-correlation function is discovered as a result of motion coupling due to interchain electrostatic repulsion. After correction, the self-part of the autocorrelation function is obtained, and the calculated mean square displacement data demonstrate a two-stage diffusion process a fast one at short time lag and a slow one at long time lag. The two processes are attributed to a faster diffusion inside the cage formed by neighboring chains and a slower diffusion beyond the cage. Effects of the salt level and polyelectrolyte concentration are investigated with the comparison with the results of light scattering, showing the connection of the bimodal dynamics and the local ordering in the polyelectrolyte solution.