A time-going-backward quasidynamics method is developed for global optimization of cluster structures, and its merits are examined by a simple classical mechanics model, indicating that the probability for the system to jump over high potential barriers by this method is much higher than that by common annealing methods. The method is then used to investigate the isomers of a Lennard-Jones cluster containing 38 atoms and the C60 cluster with the Brenner potential, and can easily give the most stable structures, which are difficult to obtain by common annealing methods. In addition, for small carbon clusters C_{n} (n=21-30) , most of the potential energies optimized by this method are much lower than those obtained by a genetic algorithm.