This paper proposes a randomness-driven global particle swarm optimisation (R-dGPSO) algorithm to solve the unconstrained optimisation problems. First, an opposition learning strategy is modified and applied to the population initialisation of R-dGPSO, which is helpful to improve the quality of the initial solutions. Second, cosine mapping and random factors are utilised to adjust the inertia weight and improve the convergence of the algorithm. Third, an impact factor is incorporated into the velocity updating formula in order to regulate the impact of personal best particles and global best particle on particles' flight trajectories. Fourth, a new location updating strategy is devised to help R-dGPSO to get rid of local optima. Experimental results show that R-dGPSO can effectively accomplish the task of numerical optimisation in most cases. Furthermore, it can produce better objective function values than the other methods. Therefore, R-dGPSO is an effective numerical optimisation method for solving unconstrained optimisation problems.