Dispersion management is a technology that alternately and periodically uses fibers with opposite dispersion sign in wavelength-division multiplexing link, thus the path averaged dispersion coefficient over each period is close to zero. This paper studies the cross-phase modulational sideband instability in chain of periodic dispersion managed and lumped amplified fiber link. Analytisis and numerical simulation are applied to show that there are multi-sidebands in the dispersion managed fiber link if the path averaged dispersion exhibits the abnormal dispersion, while there is only the lowest order if the path averaged dispersion exhibits the normal dispersion. The results of analytical and numerical simulation methods are consistent.