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The finite-difference (FD) scheme is extensively applied in seismic modelling, imaging and inversion due to its advantages of large-scale parallel computing and programming. However, numerical dispersion caused by using a difference operator in substitution for the differential operator is non-negligible, which reduces the accuracy of the modelling and can lead to some misinterpretations. In addition, the computing resources required by the FD scheme is highly demanding when dealing with large models, which limits its applicability. In this paper, a new optimised FD scheme is proposed, which is based on an improved particle swarm optimisation (PSO) algorithm. We improve the conventional PSO algorithm by introducing strategies related to local learning and global learning, which contribute to accelerating the convergence rate and effectively avoiding getting trapped in local extrema. Then, the improved PSO algorithm is used to improve the conventional FD scheme. Dispersion analysis and numerical modelling demonstrate that the low-order optimised FD scheme can achieve higher accuracy than a high-order conventional operator. Compared with the conventional FD scheme and a FD scheme based on the Remez exchange algorithm, the optimised FD scheme based on the improved PSO algorithm can more efficiently suppress numerical dispersion and increase computational efficiency. [ABSTRACT FROM AUTHOR]