A new sulfonylcalixarene-based coordination container 1 was designed and synthesized from the self-assembly reaction of p-tert-butylsulfonylcalix[4]arene (TBSC), Co(II) ion, and 2,6-naphthalenedicarboxylic acid (NDC). It crystallizes in tetragonal system, space group I4/m with a = b = 30.9119(19) Å, c = 43.565(3) Å, V = 41628(6) ų, D_c = 0.731 g/cm³, M_r = 9162.36, C₃₈₄H₃₄₈Co₂₄O₁₂₆S₂₄, Z = 2, F(000) = 9384, μ = 0.566 mm^–1, the final GOOF = 1.027, R = 0.0987 and wR = 0.2474 for 7240 observed reflections with I > 2σ(I). Structural analyses indicate that 1 adopts an edge-directed octahedral geometry and consists of six TBSC-supported Co₄ tetranuclear units locating on the vertices and twelve NDC bridging ligands occupying the edges. The new compound exhibits outstanding performance for the C₂ hydrocarbons separation over CH₄.