The building-integrated wind turbine is a new technology for the utilization of wind energy in cities. Previous studies mainly focused on the wind turbines mounted on the roofs of buildings. This paper discusses the performance of Savonius wind turbines which are mounted on the edges of a high-rise building. A transient CFD method is used to investigate the performance of the turbine and the interaction flows between the turbine and the building. The influence of three main parameters, including the turbine gap, wind angle, and adjacent turbines, are considered. The variations of the turbine torque and power under different operating conditions are evaluated and explained in depth. It is found that the edge-mounted Savonius turbine has a higher coefficient of power than that operating in uniform flows; the average Cp of the turbine under 360-degree wind angles is 92.5% higher than the turbine operating in uniform flows. It is also found that the flow around the building has a great impact on turbine performance, especially when the turbine is located downwind of the building.