Among the numerous lineages of teleost fish that have independently transitioned from obligate water breathing to facultative air breathing, evolved properties of hemoglobin (Hb)–O2 transport may have been shaped by the prevalence and severity of aquatic hypoxia (which influences the extent to which fish are compelled to switch to aerial respiration) as well as the anatomical design of air-breathing structures and the cardiovascular system. Here, we examined the structure and function of Hbs in an amphibious, facultative air-breathing fish, the blue-spotted mudskipper (Boleophthalmus pectinirostris). We also characterized the genomic organization of the globin gene clusters of the species and we integrated phylogenetic and comparative genomic analyses to unravel the duplicative history of the genes that encode the subunits of structurally distinct mudskipper Hb isoforms (isoHbs). The B. pectinirostris isoHbs exhibit high intrinsic O2 affinities, similar to those of hypoxia-tolerant, water-breathing teleosts, and remarkably large Bohr effects. Genomic analysis of conserved synteny revealed that the genes that encode the α-type subunits of the two main adult isoHbs are members of paralogous gene clusters that represent products of the teleost-specific whole-genome duplication. Experiments revealed no appreciable difference in the oxygenation properties of co-expressed isoHbs in spite of extensive amino acid divergence between the alternative α-chain subunit isoforms. It therefore appears that the ability to switch between aquatic and aerial respiration does not necessarily require a division of labor between functionally distinct isoHbs with specialized oxygenation properties.