The unprecedented urbanization and the staggering development of modern information and communication technologies (ICT) demonstrate that the concept of Smart City is attractive and achievable. Beyond the scope of traditional city services and applications, Smart Cities provide urban planners and policy makers proactive and timely information to obtain a dynamic and comprehensive understanding about the rhythm of our cities. The sustainability of Smart Cities necessitates the capability of computations and data analysis at the edge of the networks, especially for mission critical applications requiring real-time information fusion and on-site decision making. Fog Computing, an extension of Cloud Computing, enables heterogeneous mobile and smart computing devices at the edge to collaborate for instant decision making. In this paper, a smart urban surveillance platform has been proposed employing a Fog Computing paradigm. Taking an urban traffic monitoring as a case study, a prototype has been built and tested. Leveraging the underlay fog network, the real-time multi-target tracking task is accomplished using the l1 target tracking algorithm. Compared with the Cloud Computing, the experimental results are very encouraging and validate the feasibility of smart urban surveillance for instant decision making using Fog Computing at the network edges.