In this paper, we reported the two-dimensional periodic nano-micro complex structures on GaP and ZnSe crystals surface created by the interference of three femtosecond laser beams. Different types of nano-patterns were obtained by arranging the laser polarization combination of the three beams. In order to understand the formation of these nanopatterns, we theoretically calculated the distributions of laser intensity and polarization. The experimental and theoretical results indicate that the long periodic microsturctures are determined by the interferential intensity pattern, and the short periodic nanostructures were determined by the interferential polarization pattern. These researches haue huge potential applications in nanopattering of semiconductors and dielectrics.