Chemical anchoring groups can modulate the connecting between metal electrode surface and central molecule. And the distribution of electronic states and charge transport in monomolecular devices energy level can also be regulated by chemical anchoring groups. Thus the introduction of different anchoring groups will inevitably have some influence on multifunctional molecular devices. Moreover, strain effect is also one of an important method for electronic property modulation of two-dimensional materials. Therefore, in this paper, three different chemical anchoring groups are combined with compressive and tensile strains, aiming to seek the dual modulation behavior on the spin-resolved transport properties of γ-graphyne molecular devices. Our calculation results suggest that the chemical anchoring groups of pyrrole (C4H5N), thiophene (C4H4S) and 1H-Phosphole (C4H5P) molecules combined with strain have a good regulation effect on the transport of designed molecular devices, which can be seen from the transmission spectra and molecular energy spectrum (MES). In addition, the dual modulation can induce spin-polarization phenomenon and the maximum of spin filtering efficiency (SFE) reaches up to 90%. Furthermore, the negative differential resistance (NDR) behavior has been achieved in the proposed device and the maximum of the peak to valley ratio (PVR) can reach up to 12.14. Our findings may provide a theoretical basis for the dual modulation of molecular junctions by chemical anchoring groups and strain for future nanoelectronic devices.