This paper investigates the stabilisation of stochastic coupled systems with time-varying delays and Lévy noise on networks (SCSTLN) via periodically intermittent control. And here, internal delays, white noise and Lévy noise are considered in the networks. To ensure stability of SCSTLN with a periodically intermittent controller, several simple and useful criteria are obtained by establishing a new differential inequality and using a graph-theoretic approach. The intensity of control is closely related to the coupling strength and the perturbed intensity of white noise and Lévy noise. In particular, the stabilisation of stochastic coupled oscillators with time-varying delays and Lévy noise on a network as a practical application of our theoretical results is studied. Finally, a numerical example about oscillators network is carried out to show the validity and feasibility of our analytical results.