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In this paper, the finite-time distributed optimisation problem for multi-agent systems (MASs) is investigated by proposing a kind of new event-based aperiodically intermittent communication strategy. Firstly, the distributed optimisation problem with the sum of local objective functions is considered. A novel finite-time event-triggered intermittent control protocol is proposed over undirected networks, and some sufficient conditions are obtained to ensure the finite-time consensus of MASs and the asymptotical solvability of the optimisation problem. Secondly, a more general distributed optimisation problem, in which the optimisation objective is the convex combination of local objective functions, is considered and we also prove that MASs can achieve consensus in finite-time and asymptotically reach the optimal solution under the proposed protocol over directed networks. Finally, two numerical examples are given to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]