In this work, we study the supersymmetric warped conformal field theory in two dimensions. We show that the Hofman-Strominger theorem on symmetry enhancement could be generalized to the supersymmetric case. More precisely, we find that within a chiral superspace $(x^+,��)$, a two-dimensional field theory with two translational invariance and a chiral scaling symmetry can have enhanced local symmetry, under the assumption that the dilation spectrum is discrete and non-negative. Similar to the pure bosonic case, there are two kinds of minimal models, one being $N=(1,0)$ supersymmetric conformal field theories, while the other being $N=1$ supersymmetric warped conformal field theories (SWCFT). We study the properties of SWCFT, including the representations of the algebra, the space of states and the correlation functions of the superprimaries.

30 pages