To investigate the effect of permeability on turbulent wake behind a cylinder in uniform flow, we conduct particle image velocimetry on turbulent wake behind permeable cylinders, which are made of mesh sheets, of different permeabilities and compare the results with those for a solid cylinder. For relatively lower permeability, turbulent wake is quite similar to the case for a solid cylinder except for a slight shift in the streamwise direction of the reversed flow region implying turbulent Kármán vortex shedding. On the other hand, for higher permeability, the structure of turbulence is qualitatively different. More concretely, turbulent Kármán vortices disappear. Interestingly, however, the momentum deficit for such flow is comparable with that of a solid cylinder. This considerable momentum deficit can be understood with isotropic turbulence caused by the flow penetrating through the mesh constructing the cylinders. These results imply that turbulent wake behind a permeable cylinder involves dynamics both of wake and grid turbulence and the latter one dominates when permeability is sufficiently high.