Mixed matrix membranes (MMMs) comprising MgO nanosheets (MgO-NSs) and AgBF4 in a comb copolymer matrix were prepared for olefin/paraffin separation. The MgO-NSs with multi-mesopores and a large surface area were synthesized via a facile, non-hydrothermal method using MgCl2 as the precursor. Two kinds of comb copolymers, poly(oxyethylene methacrylate)-g-poly(ethylene glycol) behenyl ether methacrylate (POEM-gPEGBEM) and poly(2-hydroxypropyl 2-(methacryloyloxy) ethyl phthalate)-g-poly(ethylene glycol) behenyl ether methacrylate (PHMEP-g-PEGBEM), were synthesized via low-cost, free-radical polymerization. The neat copolymer membranes showed poor separation efficiency (selectivity of 1.0), which was improved upon incorporation of AgBF4 via facilitated olefin transport. Addition of MgO-NS further enhanced the separation performance due to the dual-functionality, i.e., the enhanced activity of the silver carrier derived from its specific interaction with silver and increased diffusivity due to the mesoporous structure. The gas separation efficacy of the PHMEP-g-PEGBEM-based membranes was superior to that of the POEM-g-PEGBEM-based membranes, indicating the effectiveness of the PHMEP chain having the phthalate group for olefin separation due to strong chelation. The MMM consisting of PHMEP-g-PEGBEM/AgBF4/MgO-NS exhibited the optimal performance, (permeance of 11.8 GPU and selectivity of 12.9) for separation of the propylene/propane mixture. The specific interaction and morphological properties of the MMMs were characterized by various spectroscopic techniques.