Aiming at the nonlinear design optimization problems with multiple constraints in the field of engineering shape design, an Adaptive Gaussian Quantum-behaved Particle Swarm Optimization (AG-QPSO) algorithm was proposed. By adjusting the Gaussian distribution adaptively, AG-QPSO algorithm was able to have strong global search ability at the initial stage of search process, and with the search process continued, the algorithm was able to have stronger local search ability, so as to meet the demands of the algorithm at different stages of the search process. In order to verify the effectiveness of the algorithm, 50 rounds of independent experiments were carried out on the two engineering constraint optimization problems: pressure vessel design and tension string design. The experimental results show that AG-QPSO algorithm achieves the average result of 5 890.931 5 and the optimal result of 5 885.332 8 on the pressure vessel design problem, and achieves the average result of 0.010 96 and the optimal result of 0.010 96 on the tension string design problem, which are better than the results of the existing algorithms such as the standard Particle Swarm Optimization (PSO) algorithm, Quantum Particle Swarm Optimization (QPSO) algorithm and Gaussian Quantum-behaved Particle Swarm Optimization (G-QPSO) algorithm. At the same time, the small variance of the results obtained by AG-QPSO algorithm indicates that the algorithm is very robust.