Abstarct: In this thesis, a new method of variational iteration method for solving first order system of differential equations are introduced. This approach, unlike the classical method, restricted variations in nonlinear exxpressions is usesd. The method compared to the classical method with generalized lagrange multipliears which reduces the computation and obtain faster result.To confirm the new method for solving linear and nonlinear differential equations, we provide examples that demonstrate the use of generalized lagrange multipliear is more reliable. The variational iteration method for initial and boundary value problems apply. A new algorithm for linear and nonlinear boundary value problems that dose not require the use of the Green funection is introduced.