Mobile edge computing (MEC) has revolutionized the way computational tasks are offloaded and latency is reduced by leveraging edge servers close to end devices. Efficient resource allocation and task offloading are crucial for enhancing system performance in MEC environments. Traditional reinforcement learning (RL) approaches have shown promise in optimizing resource allocation and task offloading problems. However, they often face challenges such as high computational complexity and the need for extensive training data. Quantum reinforcement learning (QRL) emerges as a promising solution to overcome these limitations by leveraging quantum computing principles to enhance efficiency and scalability. In this paper, we propose a hybrid quantum-classical non-sequential model for joint resource allocation and task offloading in MEC systems. Our model combines the advantages of RL in handling environmental dynamics and quantum computing in reducing adjustable parameters and accelerating the training process. Extensive experiments demonstrate that our proposed algorithm can achieve higher training and inference performance under various parameter settings compared to traditional RL models and previous QRL models.