Developing bioseparation media with both high strength and high surface area capable of efficiently separating proteins is a significant challenge. In this study, nanofibrous membranes (NFMs) with mechanical strength up to 10.8 MPa were successfully prepared by using a simple hot pressing and cross-linking process. Subsequently, mixed-mode chromatography (MMC) with both electrostatic and hydrophobic interactions was achieved by introducing glutaric anhydride (GA) onto the surface of the regenerated cellulose (RC) nanofibers. The separation of lysozyme using MMC membranes showed that the static adsorption of lysozyme (1 mg/mL) on RC-g-GA NFM reached 254 mg/g. The dynamic binding capacity of lysozyme in the flow-through mode at 10% breakthrough was 72.8 mg/g. Meanwhile, additionally, the RC-g-GA NFM could saturate lysozyme (3 mg/mL) adsorption up to 336 mg/g after 6 h of adsorption time. Moreover, the membrane could isolate lysozyme with 85% purity from a mixed solution of lysozyme and γ-globulin. This work demonstrates that RC-g-GA NFM has an efficient lysozyme isolation capability and potential for scale-up applications.