The analyses of kinematic wave properties of a new dynamics model for traffic flow are carried out. The model does not exhibit the problem that one characteristic speed is always greater than macroscopic traffic speed, and therefore satisfies the requirement that traffic flow is anisotropic. Linear stability analysis shows that the model is stable under certain condition and the condition is obtained. The analyses also indicate that the model has a hierarchy of first and second order waves, and allows the existence of both smooth traveling wave and shock wave. However, the model has a distinctive criterion of shock wave compared with other dynamics models, and the distinction makes the model more realistic in dealing with some traffic problems such as wrong-way travel analysis.