The conductance of carbon atomic wire in the environment of $H_2O$ molecules is studied by the non-equilibrium Green function method  based on density functional theory. In particular,  the carbon wire with seven atoms sandwiched between the Al(100) electrodes is considered. It is found that the transport properties are sensitive to the variation of the number and the position of the $H_2O$ molecule adsorbed on the carbon wire. To our surprise, with different positions of a single $H_2O$ molecule on the carbon wire, the equilibrium conductance shows an evident odd-even oscillatory behavior. For example, the equilibrium conductance  of the  carbon wire becomes bigger when the $H_2O$ is adsorbed on the odd-numbered carbon atoms; an opposite conclusion is obtained for the $H_2O$ adsorbed on the even-numbered carbon atoms. For the cases of two $H_2O$ molecules, the equilibrium conductance varies largely and the contribution of the third eigenchannel becomes larger in some special configurations. The above behavior is analyzed via the charge transfer and the density of states (DOS). Reasonable explanations are presented.