In the petrochemical industry, it is critical to separate the light olefins/paraffins mixtures via an efficient and economic method. In this work, a series of deep eutectic solvents (DESs) (choline chloride (ChCl)-glycerol (G), ChCl-ethylene glycol (EG), 1-butyl-3-methylimidazolium chloride ([Bmim] [Cl])-G, and [Bmim] [Cl]-EG) dissolving CuCl were used as novel membrane liquids to fabricate supported liquid membranes (SLMs) for the C2H4/C2H6 mixture separation. Interactions based on a hydrogen bond network in different DESs were characterized by time-of-flight mass spectroscopy (TOF-MS), nuclear magnetic resonance (H-1 NMR), and Fourier transform infrared (FT-IR) spectroscopy. Moreover, by absorption experiments, the Cu+ activity was quantitatively described based on a first-order equilibrium model. The effects of DESs species, CuCl concentration, transmembrane pressure, temperature, and time on separation performances were investigated by C2H4/C2H6 mixture permeation experiments. CuCl/ChCl-EG-based SLMs possessed good permeability and comparable permslectivity, as well as good long-term stability, surpassing the reported polymeric membrane upper bound. Systemic study demonstrated that the strength of the hydrogen bond networks in DESs could be tailored by optimizing the combinations of the HBAs and HBDs, and eventually improved the separation performances of the CuCl/DES-based SLMs.