The interaction potential energy of Mg-CO complex was calculated by employing ab initio method in the single and double excitation coupled-cluster theory with noniterative treatment of triple excitations CCSD (T) and large basis sets. The potential energy surface expressed by an analytical function was obtained for the first time as far as we know. A single global minimum occurs at Re= 8.98a0 and θe= 119.09° at an energy of -72.21 cm-1, and the potential energy surface has a weak anisotropy. Based on the potential, the rovibrational energy level structure of the Mg-CO complex was investigated. The microwave transition frequencies and spectroscopic parameters for the Mg-CO complex were theoretically predicted.