The Jacobi matrix required for second-order iterations, such as standard Newton–Raphson procedures, is often too costly to determine for large systems of non-linear equations of a dynamic economic model. In such circumstances, first-order iterative methods are commonly adopted. The problem then, however, is that baseline first-order iterations may not converge. This paper provides a solution to this problem by developing a hybrid method of first- and second-order iterations for solving large-scale dynamic models. The modified algorithm is robust and fast and relative running times increase with the size and complexity of the economic model. As it is easy to implement – only using standard numerical procedures to augment conventional and intuitive first-order iterations – the algorithm is particularly attractive.