Haemoglobin (Hb) is an iron-containing metalloprotein which plays a major role in the transportation of oxygen from the lungs to tissues and of carbon dioxide back to the lungs. Hb is in equilibrium between low-affinity tense (T) and high-affinity relaxed (R) states associated with its unliganded and liganded forms, respectively. Mammalian species can be classified into two groups on the basis of whether they express `high' or `low' oxygen-affinity Hbs. Although Hbs from the former group have been studied extensively, a more limited number of structural studies have been performed for low oxygen-affinity Hbs. Here, the crystal structure of low oxygen-affinity cat methaemoglobin (metHb) has been solved at 2.0 and 2.4 Å resolution in two different crystal forms. Even though both structures are fully liganded, they unusually adopt a T-state-like quaternary conformation but with several localized R-like tertiary-structural and quaternary-structural features. The study provides atomic-level insights into the ligand-binding properties of this Hb, including its low cooperativity, blunt response to allosteric effectors and low affinity for oxygen, as well as further contributing to the mechanism underlying Hb allostery.