A new kind of quantum ant colony algorithm for continuous space optimization is proposed in this paper, by the introduction of quantum computation into ant colony optimization. Each ant carries a group of quantum bits representing the current location of ant, and quantum bits are updated by quantum rotation gates to make the location of ants changed, some quantum bits are mutated by quantum non-gates to increase the population diversity in this algorithm. The convergence of proposed algorithm is proved theoretically. The numerical simulation results show that the new algorithm has better global search capability and faster convergence rate than classical ant colony optimization. Furthermore, the new algorithm is applied to the optimal design of an induction motor successfully, and optimization results are obtained. An effective design method for induction motor has been suggested based on continuous quantum ant colony optimization.