The crystal structure of the Ag-exchanged form of the zirconosilicate with the simplified formula (Na_6-2xCa_x▯_x)Zr₃[Si₉O₂₇] with x < 1 (the idealized formula Na₆Zr₃[Si₉O₂₇]), a product of thermal transformation of catapleiite, ideally Na₂Zr[Si₃O₉]·2H₂O, was studied using single crystal X-ray diffraction data. The crystal structure of Na₆Zr₃[Si₉O₂₇] is based on a heteropolyhedral framework built by nine-membered tetrahedral rings [Si₉O₂₇] and isolated [ZrO₆] octahedra. This zirconosilicate demonstrates high exchange capacity to Ag (experiment with 1 M AgNO₃ aqueous solution, 250 °C, 30 days). Its Ag-exchanged form with the simplified formula (Ag₅Ca_0.5)Zr₃[Si₉O₂₇] is characterized by a significant distortion of the heteropolyhedral framework and strongly disordered arrangement of extra-framework cations (Ag) which results in the doubling of a parameter of the hexagonal unit cell [a = 23.3462(3), c = 10.10640(10) Å, V = 4770.45(13) ų] and space group P6₃cm. Ag⁺ cations preferably occupy the sites that are close to the Na sites in Na₆Zr₃[Si₉O₂₇].