To improve computation speed and efficiency of genetic algorithm-partial square least (GA-PLS), a novel feature selection algorithm which combines quantum computation and GA-PLS (QGA-PLS) was proposed. In QGA-PLS algorithm, qubits and superposition of states were used for chromosome code. Quantum rotation gate was used for genetic operation to update parameters and enhance population diversity. Meanwhile, with PLS model which was reconstructed by quantum computing, the value of individual adaptability was calculated. Rapid convergence and good global optimization capability characterize the performance of QGA-PLS. The proposed method was applied to two simulation experiments, extreme value of a function and feature selection for Iris dataset. The experimental results indicated that, compared with QGA and GA-PLS, QGA-PLS has better performance in feature selection, execution time and classification accuracy, which proves the efficiency of proposed method.