The Network-on-Chip has been recognized as a paradigm to solve System-on-Chip (SoC) design challenges. The routing algorithm is one of key researches of a NoC design.Its importance and effect on the performance of the network is accordingly cardinal.Highperformance,load-blance,deadlock-free and livelock-free, fault-tolerant are the desirable properties of a routing algorithm for NoC.In this paper ,we summarize routing algorithms used for NoC by simply comparison and analysis,and give the merits and demerits of some routing algorithms.