Accurate estimation of the amount of rill erosion, which is generally the main erosion pattern on the hill-slope, is essential for hill-slope erosion studies. Rose et al. (2007) developed an approximate analytical solution for over land erosion processes. It is based on the averaged overland flow concept that does not consider the difference between rill flow and inter-rill processes. Focusing on the dynamic erosion characteristics of the rill, this paper expands the work of Rose and derives an improved approximate analytic solution for fully develop drill flow. This solution considers the influence of the bare soil erosion at the rill channel sides and the change of hydraulic radius, and it can return to Rose's solution automatically in the case of inter-rill erosion or generalize overland erosion situation. Laboratory experimental data on rill erosion by Lei et al. (2009) is employed to verify the solution, showing a good agreement except some very steep situations. The contribution of lateral erosion from the rill is studied and the influence of slope and flow discharge on it is discussed.