In this paper, MAPLE 18 codes are used to utilize Variational Iteration method for the numerical solution of two species Lotka-Volterra prey-predator interaction species which are governed by a system of nonlinear differential equations. Two examples are provided to show the ability and reliability of the method. The obtained approximate solution shows that Variational Iteration Method (VIM) is powerful numerical technique for solving a system of nonlinear differential equation, which can be easily applied to other nonlinear problems in biomathematics. This technique has shown to be very effective and yields accurate results.