Electroosmotic flowthrough a nano tube andnanochannelhasmanyapplications inbiomechanics and other sciences. Electroosmosis is themovement of solvent togetherwith solute under an applied electric field. For solving of theGoverning equations on Electroosmotic flowwe can use some semi analytical methods such as Reconstruction ofVariational IterationMethod (RVIM).Unlike perturbationmethod the RVIMis independent of small parameters.RVIMtechnique is a powerful and convenient algorithmin finding the approximate solutions for the linear and nonlinear equations.WhileRVIMis capable of reducing the size of calculation, it omits the difficultyarising in calculating nonlinear intricately terms.Also, it overcomes the difficulty of theAdomian polynomials by applying LaplaceTransformand avoiding the use of Lagrange multiplier. In this paper, Poisson-Boltzmann equation has been investigated. This equation is employed in electrokinetic phenomena. Poisson-Boltzmann equation for a 30 nmdiameter nano tube has been solved on the curvilinear coordinates.RVIMis applied and it is shown that accuracy and convergence of the results is good.