Scale-free property, which means a small number of nodes dominate a network with far more number of connections than other nodes, has been observed in many large-scale real-world networks and many large software systems. However, this is not investigated for answer set programming (ASP), a major paradigm of declarative problem solving. This paper first presents a generator (model) for randomly generating ASP programs that demonstrate scale-free property. Then reports that all the 28 real ASP programs from different domain showing clear scale-free property. Finally significant experiments are conducted to demonstrate that random generated ASP programs could be solved in polynomial time if they are scale-free, while general random ASP programs are NP hard problems. The results may help to understand the nature of large ASP programs.