Structure design of proton exchange membrane determines the performance of vanadium redox flow battery. Appropriate pore size of the membrane not only benefits the proton conduction but also blocks the cross contamination of the vanadium cations. For this purpose, hydration sizes of proton, vanadium (II) [V2+], vanadium(III) [V3+], oxovanadium(IV) [VO2+], and dioxovanadium(V) [VO2+] cations were estimated by molecular dynamics simulation based on all-atom force field. The local hydration structures of the vanadium cations were consistent with the previous reports, verifying the adopted force field. V2+, V3+, VO2+, VO2+, and proton exhibit the hydration sizes of 8.24, 8.14, 8.18, 8.34, and 4.12 angstrom in the aqueous mixtures of sulfuric acid and vanadium sulfate. Thus the pore size distribution from 4.12 to 8.14 angstrom was recommended for the membrane fabrication. SO42- prefers to distribute around the vanadium cations due to electrostatic interaction, thus weakening the hydration structures of the vanadium cations. Introducing sulfuric acid decreases the local distributions of SO42- around and V3+, but increases the local distributions of SO42- around VO2+ and VO2+. This work helps to understand the structure of the aqueous mixtures of sulfuric acid and vanadium sulfate. It also provides potential guidance for improving the membrane performance in vanadium redox flow battery. (C) 2018 Elsevier Ltd. All rights reserved.