This paper represents an efficient approach for solving approximated solution of the second-order nonlinear systems of differential equations using piecewise constant argument methods. A system of differential equations with piecewise constant arguments that depends on a positive integer n is introduced. It is proved that this system of equations has a unique piecewise solution, which is an approximate solution to the considered initial value problem for large n. Numerical results are presented on examples that demonstrate the effectiveness and high accuracy of the proposed method.