A new variant of Newton type methods has been developed for quantitative microwave imaging. To deal with the ill-posedness of the inverse problems, standard Newton type methods involve a linearization of the so called data equation using the Fréchet derivative with respect to the contrast function. Here, the formulation is expanded to include the object equation, therefore, the formulation seeks to reduce the errors in both the data and the object equations. While this modification does not remove the need to solve forward problem at each step, it nevertheless significantly improves convergence rate and the performance. To assess the efficiency of the proposed technique, numerical simulations with synthetic and experimental data have been carried out. The results demonstrate that the proposed variant outperforms the standard Newton method, and shows comparable performance to the contrast source inversion (CSI) algorithm with fewer iterations.