This paper is concerned on analytical treatment of non-linear differential equation of a viscous boundary layer flow due to a moving sheet. An analytic approximate technique, namely Optimal Homotopy Asymptotic Method (OHAM) is employed into a new version for this purpose. It is proved that OHAM provide accurate solution for the nonlinear differential equation of the third-order with initial and boundary conditions. Our procedure provides us with a convenient way to optimally control the convergence of the solution, such that the accuracy is always guaranteed. An excellent agreement of the approximate solution with the numerical results has been demonstrated. This work shows the general validity and the great potential of the OHAM for solving strongly nonlinear differential equation.