Researches of neuroimaging have revealed that there are many differences between left hemisphere and right hemisphere both in anatomical structure and in cognitive function. However, little is known about the topological organization of the functional networks of the two hemispheres. In the present study, we used functional magnetic resonance imaging to examine the topological organization and hemispheric differences in the functional networks in the two hemispheres. Analysis of asymmetry on functional networks was performed on a group of 192 healthy right-handed Chinese subjects. It revealed that both left and right hemisphere showed small-worldness features. We also found a significant rightward asymmetry on clustering coefficients and characteristic path length, a significant leftward asymmetry on global efficiency. In addition, the right hemisphere shows a stronger tendency of organizational modularity. These results may explain some differences in behaviors and cognition.