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In this paper we present a new analytical physics-based drain current model for fully overlapped and partially overlapped lightly-doped-drain metal-oxide-semiconductor field-effect-transistors (LDD MOSFETs). The model was developed by starting from a two-dimensional Poisson equation, and including the effects of series resistances and velocity saturation. In particular the phenomenon of surface accumulation and depletion in the LDD region is included in the model to describe saturation I-Vcharacteristics. The device is partitioned into the source, intrinsic channel, subdiffusion, and overlapped and non-overlapped lightly-doped drain regions. The device parameters such as local threshold voltage and doping concentration are continuous along the channel. The model can describe the I-Vcharacteristics and can be used to calculate the electric fields in the channel region and in the LDD region for the device operated in both the linear and saturation regions. The accuracy of the presented model has been verified by the simulated data using a fully numerical 2D simulator and the experimental data of LDD devices with various geometries.