(In,Fe)Sb layers with a Fe content up to 13 at. % have been grown on (001) GaAs substrates using the pulsed laser deposition. Transmission electron microscopy shows that the layers are epitaxial and free of second-phase inclusions. The observation of hysteretic magnetoresistance curves at temperatures up to 300 K and the investigations of magnetic circular dichroism reveal that the Curie point lies above room temperature. The resonant character of magnetic circular dichroism confirms the intrinsic ferromagnetism in the (In,Fe)Sb matrix. We suggest that the ferromagnetism of the (In,Fe)Sb matrix is not carrier-mediated and is apparently determined by the mechanism of superexchange interaction between Fe atoms.