  In the Hermitian regime, the Wannier-Stark ladder characterizes the
eigenstates of an electron in a periodic potential with an applied static
electric field. In this work, we extend this concept to the complex regime for
a periodic non-Hermitian system under a linear potential. We show that although
the energy levels can be complex, they are still equally spaced by a real Bloch
frequency. This ensures single-particle Bloch oscillations with a damping (or
growing) rate. The system can also support standard two-particle Bloch
oscillations under certain conditions. We propose two types of dimerized
non-Hermitian systems to demonstrate our results. In addition, we also propose
a scheme to demonstrate the results of electron-pair dynamics in a
single-particle 2D $\mathcal{PT}$-symmetric square lattice.
