We have studied electronic and magnetic structure of Mn-dimer molecule using OpenMX method based on density functional method. The calculated density of states shows that the four O atoms split $e_g$ and $t_{2g}$ energy levels. The energy splitting by the crystal field is smaller than bulk MnO with cubic structure, because of small coordination number of atoms. Total energy with antiferromagnetic spin configuration is lower than that of ferromagnetic configurations. Calculated exchange interaction J between Mn atoms is one order larger than that of the other Mn-O magnetic molecules. That comes from the direct exchange interaction between Mn 3d orbitals and the super-exchange interactions caused by strong ${sigma}$-bonding of Mn-O orbitals.