Based on a spirocyclic tetraether derived from pentaerythritol and [1,1′-binaphthalene]-2,2′-diol, three porous organic polymers (SPOP-7∼9) were prepared through Suzuki reaction, Sonogashira–Hagihara reaction, and thiophene-based oxidative coupling polymerization, respectively. According to the obtained nitrogen physisorption isotherms, these polymers show permanent microporous nature with the Brunauer–Emmett–Teller specific surface area varying between 280 and 860 m2 g−1. Uptake capacities of the polymers for gases (hydrogen and carbon dioxide) were also studied. Polymer SPOP-9 prepared by oxidative coupling polymerization possesses the highest carbon dioxide adsorption capacity (12.6 wt %) among the three polymers at 1.0 bar and 273 K. Polymer SPOP-7 shows moderate hydrogen adsorption capacity (1.43 wt %) at 1.0 bar and 77 K.