Aiming at achieving smooth gait transition for quadruped robots, we present a Hopf oscillator-based Central Pattern Generator (CPG) with controllable phase relationships in this paper. The proposed CPG controller can facilitate changing parameters to generate different locomotion gaits. Particularly, required phase relationships between every two oscillators can be obtained by modulating the duty factor and relative phases of legs. Therefore, smooth rhythmic signals for gait transition are generated. Moreover, the onset of the gait transition can be designed accurately. Finally, we verify the effectiveness of our controller on a simulated quadruped robot. Smooth and stable transition among walk, trot and pace gait has been achieved. Both transition from walk to trot and trot to pace are finished in a second.