Wind-tunnel experiments are performed to investigate the effect of minor modifications to the roof edge shape on the power performance and wake characteristics of a horizontal-axis wind turbine sited on a cube-shaped building. Three roof edge shapes are considered: a sharp edge, a rounded edge, and a solid fence. The power performance of the turbine is dependent on its streamwise position, and on the roof edge shape due to the difference in the flow shear induced by different roof edges. The sharp edge and solid fence cases show high variation in power with the turbine position, which is reduced significantly in the rounded-edge case. The turbine shows the worst power performance regardless of its position in the fence case. The roof edge shape is also found to affect the wind turbine wake. Specifically, the wake recovery and expansion rates are found to be greatest for the fence case, and they decrease with the increasing smoothness of the roof edges. This is related to the difference in the base flow turbulence induced by different roof edge shapes. Compared to the base flow, turbulence intensity in the wake is reduced on the building, except at the rotor top tip level.