A Zn4O clusters based flexible doubly interpenetrated metal-organic framework [(Zn4O)2(DCPB)6DMF]·2DMF·8H2O (JLU-Liu33, H2DCPB = 1,3-di(4-carboxyphenyl)benzene, DMF = N,N-dimethylformamide) with pcu topology has been solvothermally synthesized. Because of its flexible structure, JLU-Liu33 exhibits a breathing behavior upon N2 and CO2 adsorption at low temperature, and C2H6 and C3H8 adsorption at 273 and 298 K. Furthermore, by adopting the direct synthesis method, two isomorphic compounds-JLU-Liu33L and JLU-Liu33H-have been obtained by partial substituting Zn with different amounts of Co into the JLU-Liu33 framework. The gas adsorption study of Co-doped materials reveals that the gate opening effect of JLU-Liu33 can be modulated by introducing different contents of Co2+ into Zn4O clusters. Meanwhile, with the increasing amount of Co2+, the adsorption amount and isosteric enthalpy values for CO2 have been improved. It is worth mentioning that JLU-Liu33H exhibits commendable selectivity for CO2 over CH4 which may be a good candidate for industrial gas purification and air separation applications.