Many current traffic management schemes are tested and implemented using traffic simulation. An Origin-Destination (OD) matrix is an ideal input for such simulations. The underlying travel demand pattern produces observed link counts. One could use these counts to reconstruct the OD matrix. An offline approach to estimate a static OD matrix over the peak period for freeway sections using these counts is proposed in this research. Almost all the offline methods use linear models to approximate the relationship between the on-ramp and off-ramp counts. Previous work indicates that the use of a traffic flow model embedded in a search routine performs better than these linear models. In this research, that approach is enhanced using a microscopic traffic simulator, AIMSUN, and a gradient-based optimization routine, MINOS, interfaced to estimate an OD matrix. The problem is highly non-linear and non-smooth, and the optimization routine finds multiple local minima, but cannot guarantee a global minima. However, with a number of starting ¿seed¿ matrices, an OD matrix with a good fit in terms of reproducing traffic counts can be estimated. The dominance of the mainline counts in the OD estimation and an identifiability issue is indicated from the experiments. The quality of the estimates improves as the pecification error, introduced due to the discrepancy between AIMSUN and the real-world process that generates the on-ramp and off-ramp counts, reduces.