This paper first presents the occurrence of Hopf bifurcation and chaos in a practical synchronous reluctance motor drive system. Based on the derived nonlinear system equation, the bifurcation analysis shows that the system loses stability via Hopf bifurcation when the d-axis component of its three-phase motor voltages loses its control. Moreover, the corresponding Lyapunov exponent calculation further proves the existence of chaos. Finally, computer simulations and experimental results are used to support the theoretical analysis.