The rapid development of mobile communication technologies and Internet of Things (IoT) devices has introduced new challenges for multi-access edge computing (MEC). A key issue is how to efficiently manage MEC resources and determine the optimal offloading strategy between edge servers and user devices, while also protecting user privacy and thereby improving the Quality of Service (QoS). To address this issue, this paper investigates a privacy-preserving computation offloading scheme, designed to maximize QoS by comprehensively considering privacy protection, delay, energy consumption, and the task discard rate of user devices. We first formalize the privacy issue by introducing the concept of privacy entropy. Then, based on quantified indicators, a multi-objective optimization problem is established. To find an optimal solution to this problem, this paper proposes a computation offloading algorithm based on the Twin delayed deep deterministic policy gradient (TD3-SN-PER), which integrates clipped double-Q learning, prioritized experience replay, and state normalization techniques. Finally, the proposed method is evaluated through simulation analysis. The experimental results demonstrate that our approach can effectively balance multiple performance metrics to achieve optimal QoS.