An exact analytic model for undoped (or lightly doped) body MOSFETs has been derived in this paper by incorporating the mobile charge density in the 1-D Poisson's equation. The formulation starts with deriving a close form solution that relates the channel band bending and inversion charge to gate and channel voltage using Gauss's law and the gradient equation of the field effect devices. A continuous current-voltage model is then developed based on the exaction solution to the channel charge. The preliminary model has been verified by comparing with long channel results generated by 2-D simulator. Very good agreements in all operation regions from sub-threshold to strong inversion, and from linear to saturation are obtained. By using simple geometry parameter alone, the model is capable to capture all features obtained from 2-D device simulator.