A non-Hermitian version of Rashba Hamiltonian has been introduced. The said Hamiltonian is found to be pseudo-Hermitian under fermionic time-reversal and its eigen-states show a kind of two-parameter-bi-orthogonality. The possibility of an equivalent version of Kramers’ degeneracy theorem has been explored and the supersymmetric and pseudo-supersymmetric structures relating to the present system are also discussed.