It is critical for the construction party to meet the established economic and social demand for the construction project with the shortest construction period and the lowest cost. In this study, the construction characteristics of the project were analyzed. In addition, the multiconstraint and multitarget construction optimization model with minimum period and cost was established based on the quantum genetic algorithm. In order to improve the adaptability of the quantum genetic algorithm for the multiobjective model, the encoding form, quantum revolving door, and genetic flow of the algorithm were reconstructed. MATLAB 2016b was used as the simulation platform, and the implementation of the algorithm was improved according to the characteristics of the variables in the construction project, including period and cost. Finally, the optimization of the algorithm was verified and analyzed by an engineering example. The results showed that using the multiobjective quantum genetic algorithm, the optimal duration/cost can be achieved and the most reasonable and effective control decision scheme for the construction management can be provided through the Pareto solution set.