We report Zn-doping effect in the parent and F-doped LaFeAsO oxy-arsenides. Slight Zn doping in LaFe1−xZnxAsO drastically suppresses the resistivity anomaly around 150K associated with the antiferromagnetic (AFM) spin density wave (SDW) in the parent compound. The measurements of magnetic susceptibility and thermopower confirm further the effect of Zn doping on AFM order. Meanwhile Zn doping does not affect or even enhances the Tc of LaFe1−xZnxAsO0.9F0.1, in contrast to the effect of Zn doping in high-Tc cuprates. We found that the solubility of Zn content (x) is limited to less than 0.1 in both systems and further Zn doping (i.e. x > 0.1) causes phase separation. Our study clearly indicates that the non-magnetic impurity of Zn2+ ions doped in the Fe2As2 layers affects selectively the AFM order and superconductivity remains robust against the Zn doping in the F-doped superconductors.