In this study, mixed-matrix membranes (MMMs) containing MgO nanosheets (MgO-NSs) and AgBF4 in a comb copolymer matrix were successfully prepared for olefin/paraffin separation. The MgO-NSs, which were synthesized via a non-hydrothermal method, showed a large surface area with multi-mesopores. Two kinds of comb copolymers, POEM-g-PEGBEM and PHMEP-g-PEGBEM, were used as a matrix for dispersion of the MgO-NSs and AgBF4. The separation efficiency was enhanced by addition of MgO-NSs due to the dual-functionality. MgO-NSs resulted in the enhancement of the activity of silver through specific interaction and also led to increased diffusivity due to its mesoporous structure. The interactions among the MgO-NSs, silver ions, and polymer matrix were systematically characterized by using FT-IR, XPS, SAXS, and XRD analysis.