Membrane separation technology holds great potential for CO2 capture and H2 separation due to its simplified process, low energy consumption, and environmental benefits. Consequently, there is a pressing demand for membranes with ultra-high gas separation performance that can surpass the Robeson upper bound. To address this challenge, mixed matrix membranes (MMMs) were designed by combining rigid bridging ring polymerTro<spacing diaeresis>ger's base (TB) polymer with UiO-66 or UiO-66-Br to enhance gas separation properties of membranes. DFT calculations reveal that the interaction energy between UiO-66-Br ligands and TB is significantly lower than that of UiO-66 ligands with TB, suggesting the stronger interaction between the UiO-66-Br and TB polymer. The addition of UiO-66-Br enhances gas separation performance by providing additional gas transport pathways and increasing molecular sieving through its optimized pore size and functional groups. As a result, MMMs with a 40.0 wt% MOF loading exhibit CO2 and H2 permeabilities of 764.4 and 1127.8 Barrer, respectively, along with CO2/CH4, CO2/N2, H2/CH4, and H2/N2 selectivities of 15.6, 19.1, 23.0, and 28.2, surpassing the 2008 Robeson upper bound. Compared to TB membranes, the permeability of H2 and CO2 in the MMMs increased by over 247% and 222%, demonstrating exceptional gas separation performance. The design approach in this study offers an effective pathway for fabricating MMMs with high gas separation performance for efficient CO2 capture and H2 separation.