Hydrogen bonds (HBs) play a crucial role in the physicochemical properties of ionic liquids (ILs). To date, HBs between cations and anions (Ca-An) or between cations (Ca-Ca) in ILs have been reported extensively. Here, we provided DFT evidence for the existence of HBs between anions (An-An) in the IL 1-(2-hydroxyethyl)-3-methylimidazolium 4-(2-hydroxyethyl)imidazolide [HEMIm][HEIm]. The thermodynamic stabilities of anionic, cationic, and H2O dimers together with ionic pairs were studied using potential energy scans. The results show that the cation-anion pair is the most stable one, while the HB in the anionic dimer possesses similar thermodynamic stability to the water dimer. The further geometric, spectral and electronic structure analyses demonstrate that the inter-anionic HB meets the general theoretical criteria of traditional HBs. The strength order of four HBs in complexes is cation-anion pair > H2O dimer approximate to cationic dimer > anionic dimer. The energy decomposition analysis indicates that induction and dispersion interactions are the crucial factors to overcome strong Coulomb repulsions, forming inter-anionic HBs. Finally, the presence of inter-anionic HBs in the ionic cluster has been confirmed by a global minimum search for a system containing two ionic pairs. Even though hydroxyl-functionalized cations are more likely to form HBs with anions, there are still inter-anionic HBs between hydroxyl groups in the low-lying structures. Our studies broaden the understanding of HBs in ionic liquids and support the recently proposed concept of anti-electrostatic HBs.