In this paper, the Reconstruction of Variational Iteration Method (RVIM) is used to solve the Cauchy problem. The new applied algorithm is a powerful and efficient technique in finding solutions for the linear and nonlinear equations using only few terms. The Reconstruction of Variational Iteration Method(RVIM) technique is independent of any small parameters at all. Besides, it provides us with a simple way to ensure the convergence of solution series, so that we can always get accurate enough approximations. Some examples are given to elucidate the solution procedure and reliability of the obtained results.