Abstract: Internet topology is highly orderly at its router level. According to the basic theory of Shanon's informational entropy, the Internet structure entropy and Internet standard structure entropy were computed using the Internet data provided by CAIDA skitter project. Furthermore, by simulating experiment, the changes in service efficiency, mean shortest path and standard structure entropy were also computed in the circumstance where the Internet is attacked either maliciously or randomly, thus revealing that the scale-free Internet topology is just the main influencing factor on the robustness of Internet. It is seen from the experimental result that Internet is robust to random attack but frail to vicious attack because it has a scale-free effect.