This paper investigated a simple three dimensional nonlinear differentiable dynamical system with an absolute value term, whose boundary condition of the first Hopf bifurcation was derived by the Lyapunov method.Nonlinear dynamics techniques,such as phase portrait,bifurcation diagram and largest Lyapunov exponent spectrum,were employed to analyze the bifurcation and chaos features of the system.The chaotic patterns of the system were found to be resulted from Feigenbaum route, and the period windows existed inside the chaos region.When the controlling parameter passes the crisis critical value,the unstable periodic trajectory encounters with the chaotic attractor on the attractor's boundary,which results in boundary crisis.Transient chaos also occurs during a relative long time,when the parameter,during a little range,is bigger than the crisis critical value.