Non-Hermitian skin effect (NHSE) is a unique feature studied extensively in noninteracting non-Hermitian systems. In this paper, we extend the NHSE originally discovered systems to interacting many-body by investigating an exactly solvable model, i.e., prototypical Lieb-Liniger Bose gas with imaginary vector potential. We show that model can also be solved through Bethe ansatz. By solving ansat...