Transfer and output characteristics of fully-depleted polycrystalline silicon thin film transistors, including both tail and deep acceptor-like trap states in bulk, in the above-threshold region with low drain bias are presented under low or high state density in the situation without or with interface charge, respectively. The characteristics are calculated by a simple surface-potential-based drain current model in the strong inversion region with valid bias condition explained, and 2D-device simulation. The above-threshold region is found to be divided into Regions I and II, with Vsi , indicating the channel beginning to be completely strongly-inverted and large currents, and explication of deviations between the model and simulation in Region I. The large-traps effect on the range of Region I and Vth in the high state density situation is discovered.