Abstract：We discuss the chaotic behavior of a kind of special map on an interval. The map is a good tool to approach problems in practice, such as digital signal processing and chaos control. To use the map for solving problems better, it is necessary to discuss its complexity. In addition, chaos is an useful concept in describing the complexity of a system. The best feature of chaotic system is that the evolution of the system is sensitive to initial conditions. Chaos in the sense of Li-Yorke and distributional chaos are relatively common. Through the method of construction and with the help of the distributional chaos for the shift on the one-sided symbolic space, we prove that the map is distributively chaotic , moreover, it is chaotic in the sense of Li-Yorke.