Abstract: We study a Bose-Einstein condensate of ultracold atoms subject to a non-Hermitian spin-orbit coupling, where the system acquires the non-Hermitian skin effect under the interplay of spin-orbit coupling and laser-induced atom loss. The presence of the non-Hermitian skin effect is confirmed through its key signatures in terms of the spectral winding under the periodic boundary condition, the accumulation of eigen wavefunctions at boundaries under an open boundary condition, and bulk dynamics signaled by a directional flow. We show that bulk dynamics, in particular, serves as a convenient signal for experimental detection. The impact of interaction and trapping potentials is also discussed based on the non-Hermitian Gross-Pitaevskii equations. Our work demonstrates that the non-Hermitian skin effect and its rich implications in topology, dynamics, and beyond are well within the reach of current cold-atom experiments.