Approximate solution of fuzzy initial value problem composed of interval fuzzy ordinary differential equation subject to initial conditions given as fuzzy intervals is the main objective of this work. The considered fuzzy initial value problem was given with Hukuhara definition of the difference and derivatives for interval-valued functions, in which two cases are considered depending on the comparison between the lower and upper functions of the solution derivative. The followed definition for presenting the fuzzy interval is generalized using trapezoidal fuzzy number, while the followed approximated method used in this work is the variational iteration method and its modification to increase the accuracy and the rate of convergence to the exact solution.