We study the negative thermal expansion (NTE) properties and effect of Na insertion on the NTE of the framework material GaFe(CN)6 by first-principles calculations based on density functional theory within the quasi-harmonic approximation.The calculated results show that the material exhibits NTE due to the low transverse vibrational modes of the CN groups.The modes demonstrate larger negative values of the mode Griineisen parameters.Once Na is introduced in the framework of the material,it prefers to locate at the center of the quadrates of the framework material and binds to the four N anions nearby.As a consequence,the transverse vibrational mode of the CN group is clearly hindered and the NTE of the material is weakened.Our theoretical calculations have clarified the mechanisms of NTE and the effect of the guest Na on the NTE of the framework material.