The Turkish Strait System, which is the only connection between the Black Sea and the Mediterranean Sea, is a challenging region for ocean circulation models due to topographic constraints and water mass structure. We present a newly developed high resolution unstructured finite element grid model to simulate the Turkish Strait System using realistic atmospheric forcing and lateral open boundary conditions. We find that the jet flowing from the Bosphorus Strait into the Marmara creates an anticyclonic circulation. The eddy kinetic energy field is high around the jets exiting from the Bosphorus Strait, Dardanelles Strait, and also the leeward side of the islands in the Marmara Sea. The model successfully captures the two-layer structure of the Sea of Marmara. The volume transport at the Bosphorus is around 120 km${}^3$/year which is consistent with the recent observations. The largest bias in the model is at the interface depth due to the shallower mixed layer.