This paper presents the results of studies on the pervaporation properties (for benzene/hexane mixtures) and gas permeability (for He, H2, N2, O2, CO2, CH4, C2H6, and C4H10) of ladder-like polyphenylsesquioxanes (L-PPSQ) with improved physical and chemical properties. These polymers were obtained by condensation of cis-tetraphenylcyclotetrasiloxanetetraol in ammonia medium. The structure of L-PPSQ was fully confirmed by a combination of physicochemical analysis methods: 1H, 29Si NMR, IR spectroscopy, HPLC, powder XRD, and viscometry in solution. For the first time, a high molecular weight of the polymer (Mn = 238 kDa, Mw = 540 kDa) was achieved, which determines its improved mechanical properties and high potential for use in membrane separation. Using TGA and mechanical analysis methods, it was found that this polymer has high thermal (Td5% = 537 °C) and thermal-oxidative stability (Td5% = 587 °C) and good mechanical properties (Young’s module (E) = 1700 MPa, ultimate tensile stress (σ) = 44 MPa, elongation at break (ε) = 6%), which is important for making membranes workable under various conditions. The polymer showed a high separation factor for a mixture of 10% wt. benzene in n-hexane (126) at a benzene flow of 33 g/(m2h).