A new type of zeolite-based covalent organic frameworks (ZCOFs) was designed under different topologies and linkers. In this study, the silicon atoms in zeolite structures were replaced by carbon atoms in thiophene, furan, and pyrrole linkers. Through the adoption of this strategy, 300 ZCOFs structures were constructed and simulated. Overall, the specific surface area of ZCOFs is in the range of 300–3500 m2/g, whereas the pore size is distributed from 3 to 27 Å. Furthermore, the pore volume exhibits a wide range between 0.01 and 1.5 cm3/g. Screening 300 ZCOFs with the criteria towards methane storage, 11 preliminary structures were selected. In addition, the Grand Canonical Monte Carlo technique was utilized to evaluate the CH4 adsorption ability of ZCOFs in a pressure ranging from 1 to 85 bar at a temperature of 298 K. The result reveals that two ZCOF structures: JST-S 183 v/v (65–5.8 bar) and NPT-S 177 v/v (35–1 bar) are considered as potential adsorbents for methane storage. Furthermore, the thermodynamic stability of representative structures is also checked base on quantum mechanical calculations.