A family of polymer/liquid crystal (LC) composite membranes composed of poly(cis-butadiene) (PB) and diethylene glycol bis(4-(4’-ethoxybenzoyloxy)benzoate) (DEBEB) with smectic and nematic phase was prepared. The oxygen enrichment properties of the composite membranes were investigated. It was found that the relationship between permeability coefficient (P) and temperature (T) was characterized by N-shape P-T curves, that is, with increasing T, P first increased, followed by a decrease, then increased again. In addition, a composite membrane with less DEBEB content, such as 10 wt%, shows better oxygen permeabilities that those with more DEBEB content as well as a PB membrane at room temperature. The oxygen enrichment properties of the composite membrane for second measurement exhibits better results than the first measurement in a temperature range of the nematic phase of DEBEB. These phenomena were interpreted as the influence of the phase behaviour of DEBEB and the morphology of the composite membranes on the gas permeabilities.