Exploring stable adsorbents for efficient separation of C2H2 and CO2 from CH4 is of great significance to meet the requirements of natural gas upgrading and high-purity C2H2 production. Despite excellent structure stability and large surface area/pore volume, low adsorbate affinity and co-adsorption of mixtures in zirconium-organic frameworks (Zr-MOFs) seriously limit their applications in gas separation. To overcome these limitations, we designed a series of stable adsorbents based on Zr-based PCN-605 by replacing two H atoms from two central ligand-aromatic rings with different functional groups (–F, –OH, –NH2, –SO3H, and –SO3Ag), which are expected to gain steric hindrance effect and charge-tuning effect in varying degrees. The adsorption and separation performances of C2H2/CH4 and CO2/CH4 in PCN-605 materials were theoretically investigated by combining grand canonical Monte Carlo and density functional theory. Thereinto, PCN-605-SO3Ag shows the largest selectivity of C2H2/CH4 (1031.5) and CO2/CH4 (271.1) under molar ratio 1:99 at 298 K, or increased by 43.3 and 11.9 times, as against the parent PCN-605. This improvement is attributed to a good synergism of steric hindrance effect with charge-tuning effect exerted by –SO3Ag, which modifies not only the pore surface structure but also the charge distribution, favoring special three-way adsorption to recognize C2H2, strengthening CO2 affinity with –SO3Ag, but suppressing CH4 uptake, etc. This work highlights the effect of precise surface-structure and charge-distribution control by ligand functionalization on C2H2/CH4 and CO2/CH4 separation in PCN-605 materials, and provides a feasible strategy to design function-oriented Zr-MOF adsorbents for applications of natural gas upgrading and C2H2 extraction.