Abstract: Solving system of nonlinear Volterra integral equations has attracted enormous attention due to its importance in different sciences. Therefore, this study proposes a new efficient algorithm called NLVIEEIM. Specifically, the Gear Explicit method is developed to solve Systems of Nonlinear Volterra Integral Equations of the second kind (SNLVIE-2). Additionally, we used backward differentiation formula first-order implicit method to improve this solution. The algorithm is examined by numerical examples and the calculations are carried out using MATLAB 2014b Software. The outcomes show a better accuracy in solving SNLVIE-2.