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[Introduction & aim of the study] Recent experimental and theoretical studies suggest that the carbon-vacancy complexes are formed in Fe-C alloys. In this work, we have performed first-principles calculations to evaluate the stability carbon-vacancy complexes in α-Fe. For comparison, nitrogen-vacancy complexes have been investigated. [Method] We employed VASP code to obtain formation energies and stable structures of interstitial solutes Xn (X = C and N, n = 1 to 6) and vacancy (V) complexes. The chemical bonding was analyzed using DV-Xα molecular orbital calculations. [Results & conclusion] The formation energies of carbon-vacancy complexes have been calculated with reference to the total energy of an isolated interstitial atom and an isolated mono vacancy. In the case of carbon-vacancy complexes, the C2-V complex is most stable due to the energy gain by forming the C-C bonding. On the one hand, the N2-V complex is less stable than the N1-V complex. This is due to the repulsive interaction between N atoms. The overlap population analysis reveals that the C 2s – C 2s anti-binding interaction is reduced by the C 2s – C 2p bonding interaction. The interaction between the N 2s and N 2p orbitals is not strong enough to cancel the N 2s – N 2s anti-bonding interaction.