We have proposed a modified traffic model in which a single car moves through a sequence of traffic lights controlled by a step function instead of a sine function. We have found the complex behaviors in this simple traffic model and given three kinds of bifurcation diagrams. We have found that in this model there are chaotic and complex periodic motions, as well as special singularity. In this paper, we will introduce two special kinds chao which is different from general chao and the singularities of the simple traffic model. There are three different kinds of singularity which are single singularity, unsymmetic and symmetic double singularity.