We explore some interesting phenomena in a simple non-Hermitian ladder system.Special modes with energy eigenvalues closely related to the inter-chain-coupling strength appear in the non-Hermitian ladder system.We show that a phase transition occurs whereby special modes with pure real eigenvalues can switch to special modes with pure imaginary eigenvalues,when the inter-chain-coupling strength changes from symmetric to asymmetric.We find that the density profiles of all the special modes are completely identical under certain conditions,even if the inter-chain-coupling strength is added into the non-Hermitian ladder system in different ways.Moreover,we also demonstrate that the different inter-chain couplings are fundamentally equivalent to adding different on-site potential energies into the non-Hermitian ladder system.