This paper presents a novel CPG-based gait generation of the curved-leg hexapod robot that can enable smooth gait transitions between multi-mode gaits. First, the locomotion of the curved leg and instability during the gait transitions are analyzed. Then, a modified Hopf oscillator is applied in the CPG control, which can realize multiple gaits by adjusting a simple parameter. In addition, a smooth gait switching method is also proposed via smooth gait transition functions and gait planning. Tripod gait, quadruped gait, and wave gait are planned for the hexapod robot to achieve quick and stable gait transitions smoothly and continuously. MATLAB and ADAMS simulations and corresponding practical experiments are conducted. The results show that the proposed method can achieve smooth and continuous mutual gait transitions, which proves the effectiveness of the proposed CPG-based hexapod robot control.