The analysis of the theory and simulation for the complicated and abundant chaotic dynamical behavior of a three-cell coupled QCNN have been done by using the polarization of a quantum - dot cell and quantum phase as state variables and parameter b as bifurcation parameter. By the practical numerical calculation the maximal Lyapunov exponents curve, bifurcation map and power curve are obtained. The results show that the route for the system response entering into chaos is quasi - period bifurcation and that the system only has one chaos region and there is no periodical window in the chaos region.