As quantum computing technology continues to advance, various sectors, including industry, government, academia, and research, have increasingly focused on its future applications. With the integration of artificial intelligence techniques, multiple Quantum Neural Network (QNN) models have been proposed, including quantum convolutional neural networks, quantum long short-term memory networks, and quantum generative adversarial networks. Furthermore, optimization methods such as constrained optimization by linear approximation and simultaneous perturbation stochastic approximation have been explored. Therefore, this study proposes Hybrid Quantum Swarm Intelligence (HQSI), which constructs a QNN model as a forward propagation neural network. After measuring quantum states and obtaining prediction results, a classical computer-based swarm intelligence algorithm is employed for weight optimization. The training process iterates between quantum and classical computing environments. During the experimental phase, the proposed HQSI method is evaluated using an online certificate status protocol request traffic prediction task. Comparative analysis against state-of-the-art quantum optimization algorithms demonstrates that the proposed HQSI approach achieves more than a 50% reduction in error.