This study presents the crystal structure of Greyhound hemoglobin (GrHb) determined to 1.9 Å resolution. GrHb was found to crystallize with an α₁β₁ dimer in the asymmetric unit and belongs to the R2 state. Oxygen-affinity measurements combined with the fact that GrHb crystallizes in the R2 state despite the high-salt conditions used for crystallization strongly indicate that GrHb can serve as a model high-oxygen-affinity hemoglobin (Hb) for higher mammals, especially humans. Structural analysis of GrHb and its comparison with the R2-state of human Hb revealed several regions that can potentially contribute to the high oxygen affinity of GrHb and serve to rationalize the additional stability of the R2-state of GrHb. A previously well studied hydrophobic cluster of bar-headed goose Hb near α119 was also incorporated in the comparison between GrHb and human Hb. Finally, a structural comparison with generic dog Hb and maned wolf Hb was conducted, revealing that in contrast to GrHb these structures belong to the R state of Hb and raising the intriguing possibility of an additional allosteric factor co-purifying with GrHb that can modulate its quaternary structure.