As a new branch of MOFs which are composed of biocompatible metal ions and organic ligands, bio-metal-organic frameworks (bio-MOFs) have attracted much attention recently. Bio-MOFs feature multiple Lewis basic sites which have strong interaction with CO2 molecules, thus they have great potential in the separation and purification of gas mixtures containing CO2. In this work, molecular simulation studies were carried out to investigate the adsorption and diffusion behaviors of CO2/N2 gas mixtures in bio-MOF-11. Results show that bio-MOF-11 displays excellent adsorption selectivity towards CO2 in CO2/N2 gas mixtures which was dominated by electrostatic interaction between material and CO2. In addition, we found both CO2 and N2 molecules were preferably adsorbed around the pyrimidine ring and exocyclic amino and transferred to the secondary favorable adsorption sites (methyl groups) with increasing pressure. Bio-MOF-11 membranes show superior permeation selectivity, but low permeability for CO2/N2 gas systems. The reason is that the small pores restrict the movement of gas molecules, leading to the observed low permeability. The information obtained in this work can be applied to other theoretical and experimental studies of bio-MOFs adsorbents and membranes in the future.