Does download music; upload music; and share music on the Internet illegal? This subject has been sustained developed. Individuals who download music on the Internet may constitute a copy against copyright law. Individuals who offer music files on the 'master-slave structure' music sites for users to download may also constitute public transportation against copyright law. However, do people who offers decentralized P2P software providing a platform for users to share music illegal? This question is still controversial. The United States Supreme Court in 2005 has made a decision on Grokster case. After, the Taiwan's district courts have made two totally different decisions about Kuro and ezPeer around 2006, and the two cases both have been reconciled on the appeal, leaving unresolved dispute. This article studies related judgments and compares their different points and then finds out why we have such a different point. Simply put, this may be because the copyright law systems are different between U.S. and Taiwan. This paper would like to further explore more. The author will use the perspective of economic to analysis this issue. The author argues that, if we have only two options: there is liability or not, the file-sharing software should be identified be illegal. But after the P2P music-sharing software is illegal, and the legal protection of the network environment will enough, do the record companies really willing to enter the Internet market? It is questionable. This paper will also be a simple forecast the online music market development.