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This paper proposes a novel randomly adapting particle swarm optimization (RAPSO) approach which uses a weighed particle in a swarm to solve multi-dimensional optimization problems. In the proposed method, the strategy of the RAPSO acquires the benefit from a weighed particle to achieve optimal position in explorative and exploitative search. The weighed particle provides a better direction of search and avoids trapping in local solution during the optimization process. The simulation results show the effectiveness of the RAPSO, which outperforms the traditional PSO method, cooperative random learning particle swarm optimization (CRPSO), genetic algorithm (GA) and differential evolution (DE) on the 6 benchmark functions.