In order to investigate the heterogeneous-interface characteristics between LaS/CeS and γ-Fe, the edge-to-edge matching (E2EM) model was employed to calculate the atomic matching mismatch between LaS/CeS and γ-Fe from the crystallographic point view. On the basis of the crystallographic calculations, the first-principle calculation based on the density functional theory was performed to calculate the interfacial bonding characteristics and the interface energy between LaS/CeS and γ-Fe on the atomic scale. The crystallographic calculations indicated that the minimum of the interatomic spacing misfit between LaS/CeS and γ-Fe along the matching direction was 10.63%/10.52%, and the minimum of interplanar spacing mismatch is 2.04%/3.32%, respectively. The rough orientation relationships (ORs) were predicted as follows: LaS∥γ-Fe &LaS∥γ-Fe and LaS∥γ-Fe &LaS∥γ-Fe; CeS∥γ-Fe &CeS∥γ-Fe and CeS∥γ-Fe &CeS∥γ-Fe. Based on the predicted ORs, six interface models with different atomic terminations were constructed using the coherent interface approximation. The first-principles calculations showed that the adhesion work of the interface between LaS/CeS and γ-Fe with the lowest interatomic mismatch was 4.78J·m-2/3.65J·m-2，which indicated the larger bonding strength of the interface between LaS/CeS and γ-Fe with the lower interatomic mismatch. The interface bond was dominated by the metal bond. The calculations of interface energy between LaS/CeS and γ-Fe indicated that the smaller the interatomic mismatch was, the lower the interface energy was obtained. The interface energy between LaS/CeS and γ-Fe with the lowest interatomic mismatch was -0.58J·m-2/-3.43J·m-2. The first-principles calculations can provide the theoretical foundations from the energetics point view for the crystallographic matching between LaS/CeS and γ-Fe. current method.