Maximin strategy has its origin in game theory, but it can be adopted for effective multiobjective optimization. This paper proposes a particle swarm multiobjective optimiser, maximinPSO, which uses a fitness function derived from the maximin strategy to determine Pareto-domination. The maximin fitness function has some very desirable properties with regard to multiobjective optimization. One advantage is that no additional clustering or niching technique is needed, since the maximin fitness of a solution can tell us not only if a solution is dominated or not (with respect to the rest of the population), but also if it is clustered with other solutions, i.e., diversity information. This paper demonstrates that on the ZDT test function series, maximinPSO produces an almost perfect convergence and spread of solutions towards and along the Pareto-optimal front respectively, outperforming one of the state-of-art multiobjective EA algorithms, NSGA II, in all the performance measures used.