The electroosmotic drag and the corresponding mechanism of water molecules in hydrated potassiumperfluorosulfonate electrolyte polymer membrane were studied using molecular dynamics simulations, and therelationship between the membrane structure and electroosmotic drag characteristics was analyzed. It is concluded thatvelocities of both H_{2}O and K^{+ }obey the Maxwell velocity distribution function without external electric field applied. Ifan appropriate electric field is applied, the velocities of H_{2}O and K^{+ }still obey the Maxwell velocity distribution in thedirection perpendicular to the electric field, and obey the peak shifted Maxwell velocity distribution in the directionparallel to the electric field. The peak shifting velocities coincide with the average transport velocities of H_{2}O and K^{+} induced by the applied electric field, and could be applied to evaluate the electroosmotic drag coefficient of water. Theresults also show that the average number of water molecules in the first coordination shell of K ^{+ }is 4.04, and theaverage transport velocity of these water molecules is about 57% of that of K ^{+}. The electroosmotic drag coefficientcontributed by these water molecules is about 77% of total the electroosmotic drag coefficient(2.97) .