The microwave spectrum of IBr was measured in the low rotational transition J = 3 ← 2 in order to resolve the hyperfine structure as completely as possible. Rotational constants and quadrupole coupling constants were derived for both nuclei. The observation of the rotational spectrum in different vibrational states yields the vibrational dependence of the rotational constants as well as of the hyperfine parameters. The Dunham potential coefficients a0, a1, a2, a3 are given.