We report properties of the Zn-substituted polycrystalline superconductors BaFe 1.87− x Zn x Co 0.13 As 2 (x=0, 0.04, 0.06 and 0.08) prepared at ambient pressure condition. Electrical conductivity and magnetization measurements revealed that the superconductivity is suppressed by at most 2% substitution of Zn, which shows typical behavior of an anisotropically gaped superconductivity rather than an isotropically gaped superconductivity. With increasing the amount of Zn, weak change in superconductivity was observed. It is likely impossible to obtain BaFe 1.87− x Zn x Co 0.13 As 2 crystals with x>0.04 at ambient pressure condition. On the basis of the structural and the physical properties of the present system, we discuss a possible mechanism of the superconducting pairing.