In today's world, everything is connected via the Internet. Smart cities are one application of the Internet of Things (IoT) that is aimed at making city management more efficient and effective. However, IoT devices within a smart city may collect sensitive information. Protecting sensitive information requires maintaining privacy. Existing smart city solutions have been shown not to offer effective privacy protection. We propose a novel continuous method called Differential Privacy-Preserving Smart City (DPSmartCity). When the IoT device produces sensitive data, it applies differential privacy techniques as a privacy-preserving method that uses Laplace distributions or exponential distributions. The controller receives the perturbed data and forwards it to the SDN. SDN controllers eventually send the data to the cloud for further analysis. Accordingly, if the data is not sensitive, it is directly uploaded to the cloud. In this way, DPSmartCity provides a dynamic environment from the point of view of privacy preservation. As a result, adversaries are unable to easily compromise the privacy of the devices. The solution incurs at most 10-18% overhead on IoT devices. Our solution can therefore be used for IoT devices that are capable of handling this overhead.