The defect structure of Fe28Al samples is examined with the Positron Annihilation Lifetime Spectroscopy. The studies are carried out for samples in as-cast state and after heat treatments: annealing for 24 hours at 900°C (or 1050°C) and either slow cooling with furnace or quenching to oil. The PALS spectra are analyzed using two-state trapping model. Only one type of defects is detected. The positron lifetime in these defects (V) suggests that they are quenched-in Fe-monovacancies (VFe). The vacancy concentration strongly depends on the rate of cooling. Besides, V also depends slightly on the rate of cooling of the material. This fact suggests, according to the predictions of latest theoretical calculations, that V is sensitive to the atomic configuration in the nearest neighborhood of VFe, which give hope to estimate the degree of atomic ordering in alloys by the PALS technique.