In the present study the properties of novel cation-exchange membranes based on UV-oxidized polymethylpentene (PMP) with grafted sulfonated polystyrene are described. A correlation between the composition of the grafted copolymer (grafting degree, cross-linking degree) and transport properties (Na+-conductivity, permselectivity, diffusion permeability) of resulted membranes are discussed. It is shown that with increasing of grafting degree (GD) and lowering of cross-linking degree (CD) the concentration of functional groups in the inner solution and permselectivity decrease, while ionic conductivity increases. The obtained membranes have the GD ranging from 29 to 120% and CD from 0 to 5%. The best membranes have ionic surface resistance of 0.3–0.6 Ω cm2 in 0.5 M NaCl, apparent cation transport numbers of 0.870–0.998 and NaCl diffusion permeability of 3.3 · 10−8–5.5 · 10−7 cm2 s−1, as well as satisfactory mechanical performance. A comparison of transport properties (conductivity and cation transport number) of the obtained membranes with a properties of number of available samples was made. It is noted that some of the obtained samples are at the level of the best perfluorinated homogeneous membranes in terms of the ratio of conductivity and cation transport numbers. High ionic conductivity and permselectivity make the prepared membranes promising candidates for possible applications in electrodialysis, dialysis, reverse electrodialysis, Red-Ox flow batteries and other membrane processes.