Proliferation of IoT (Internet of Things) and sensor technology has expedited the realization of Smart City. To enable necessary functions, sensors distributed across the city generate a huge volume of stream data that are crucial for controlling Smart City devices. However, due to conditions such as wears and tears, battery drain, or malicious attacks, not all data are reliable even when they are accurately measured. These data could lead to invalid and devastating consequences (e.g., failed utility or transportation services). The assessment of data reliability is necessary and challenging especially for Smart City, as it has to keep up with velocity of big data stream to provide up-to-date results. Most research on data reliability has focused on data fusion and anomaly detection that lack a quantified measure of how much the data over a period of time are adequately reliable for decision-makings. This paper alleviates these issues and presents an online approach to assessing Big stream data reliability in a timely manner. By employing a well-studied evidence-based theory, our approach provides a computational framework that assesses data reliability in terms of belief likelihoods. The framework is lightweight and easy to scale, deeming fit for streaming data. We evaluate the approach using a real application of light sensing data of 1,323,298 instances. The preliminary results are consistent with logical rationales, confirming validity of the approach.