Complex tasks require the combination of both discrete and rhythmic movements. Though scientists do not yet agree on the neural architecture involved in both types and in the transition from one to the other, the importance of having robot controllers able to behave rhythmically and discretely is universally recognized. In this paper, a bio-inspired robot controller based on oscillating neurons is proposed to realize both discrete and rhythmic movements and easily transition from one to the other. It is shown that, under certain parameter conditions, the CPG controller behaves like a PID controller. In order to demonstrate the feasibility of controlling both discrete and rhythmic movements, the CPG is applied to the initiation of handshaking, namely, reach towards the human hand and start to shake it. Results show that this architecture is suitable for both discrete and rhythmic movements and can easily transition from one to the other.