Abstract: In finite dimensional Hilbert space, the metric subregularity of a set-valued mapping, which is the difference of a continuous differentiable single valued mapping and a continuous closed convex set-valued mapping, is mainly analyzed. Firstly, under the appropriate continuous assumption, a sufficient condition for the strong metric subregularity of this kind of set-valued mappings is obtained; then, under the continuous condition of some “single value selection”, the directional metric subregularity of this type of set-valued mappings are explored, and some sufficient conditions for the directional metric subregularity of this kind of set-valued mappings are obtained.