The volume dependence of local electronic and magnetic properties of γ′-Fe4N has been investigated using the self-consistent spin-polarized linear muffin-tin orbital (LMTO) calculation. The results obtained indicate that the Fe magnetic moment at the face-centred sites (FeII) decreases more rapidly than that at the corner sites (FeI) with decreasing unit-cell volume. The decrease of Fermi-contact hyperfine field (HFC) at Fe sites with the decrease of the unit-cell volume not only results from the corresponding decrease of the Fe magnetic moment, but also is affected by the abnormal change of the transferred HFC (HFCt,val) at these sites. The discussion on HFCt,val at Fe sites partly reveals the unit-cell volume dependence of hyperfine interactions among atoms. Moreover the change of the calculated Mossbauer isomer shift (IS) at Fe sites with decreasing unit-cell volume is in agreement with the experimental results.