In this paper, we propose the use of a surrogate model based on mixtures of liner Taylor polynomials for Trust Region methods. The main objective of this model is to reduce the myopia presented in surrogate models based on single low-order Taylor expansions by which, the number of iterations during the optimization process of Trust Region based methods can be increased. The proposed model is built as follows: points are sampled from the search space, at each sampled point a surrogate model of the cost function is built by using a linear Taylor polynomial and then, cost functions can be locally approximated via a convex combination of such surrogate models. The Trust Region framework is then utilized in order to validate the quality of the proposed model. Experimental tests are performed making use of the three-dimensional variational optimization problem from data assimilation with an atmospheric general circulation model. The results reveal that, the use of our proposed surrogate model can improve the quality of the local approximations and even more, their use can decrease the number of iterations needed in order to obtain accurate solutions.