Data processing in high-dimensional spaces is a challenging task. In order to effectively classify the data in a high-dimensional space, a quantum particle swarm optimization classification algorithm (QPSOCA) for high-dimensional datasets is proposed in this paper. In QPSOCA, an uncorrelated discriminant analysis algorithm is utilized to reduce the dimension of the data, which is implemented automatically and no extra parameters are needed. In addition, to avoid the randomness of the swarm and improve the convergence speed, quantum computation is introduced into particle swarm optimization (PSO). In the experimental section, a detailed comparison of three different combinatorial optimization methods is given to demonstrate the efficiency of the proposed algorithm. Comparative experiments show that the proposed algorithm can improve the classification accuracy.