The optimal power flow (OPF) is an extremely complex, nonlinear programming (NLP) problem encountered in power system transmission planning and operations. In this paper, the application of the incremental linear programming (LP) method to the OPF is explored. A trust region method is proposed for determining the size of the optimization region for the linearized model during each iteration. Generator real power limits, reactive power limits, and bus voltage limits are included in the model. Using the proposed strategy, performance results for the IEEE 14 bus power system test case are provided. Results show that the method achieves a very fast rate of convergence to a high accuracy.