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In order to improve the global search ability and the convergence speed of the Artificial Fish Swarm Algorithm (AFSA), a novel Quantum Artificial Fish Swarm Algorithm (QAFSA) which is based on the concepts and principles of quantum computing, such as the quantum bit and quantum gate is proposed in this paper. The position of the Artificial Fish (AF) is encoded by the angle in [0, 2π] based on the qubit's polar coordinate representation in the 2-dimension Hilbert space. The quantum rotation gate is used to update the position of the AF in order to enable the AF to move and the quantum non-gate is employed to realize the mutation of the AF for the purpose of speeding up the convergence. Rapid convergence and good global search capacity characterize the performance of QAFSA. The experimental results prove that the performance of QAFSA is significantly improved compared with that of standard AFSA.