This paper constructs a third-step second-order numerical approach for solving a mathematical model on the dynamic of corruption and poverty. The stability and error estimates of the proposed technique are analyzed using the L 2 -norm. The developed algorithm is at least zero-stable and second-order accurate. Furthermore, the new method is explicit, fast and more efficient than a large class of numerical schemes applied to nonlinear systems of ordinary differential equations and can serve as a robust tool for integrating general systems of initial-value problems. Some numerical examples confirm the theory and also consider the corruption and poverty in Cameroon.