Smart City requires an intelligent and efficient network to provide services with good quality-of-experience (QoE). In this paper, we propose to develop a secure and distributed network QoE measurement for smart networks in Smart Cities. Network measurement capability has been updated gradually as the network technology progresses. For example, software-defined network will enable efficient monitoring and control of the core network. However, end-to-end network QoE measurement requires distributed approaches from the user side. In our proposed measurement framework, a traffic measurement agent is deployed in the last-hop gateway. The gateway is equipped with new features, i.e., encrypted packet classifier, traffic prediction, and user quality-of-service (QoS) to QoE mappings. Since all measurement process is done at the gateway, end user devices are separated from the entire process. Thus security can be provided by the proposed measurement framework. In addition to the framework, we demonstrated a efficient learning approach to develop the traffic prediction scheme and the QoS to QoE mapping scheme. Experiments results demonstrated that the developed schemes are applicable to a distributed network QoS measurement framework for Smart City network services.