We systematically investigate the topological properties of a one-dimensional non-Hermitian Kitaev chain with long-range coupling, where three different cases, with nonreciprocal superconducting pairing terms, nonreciprocal couplings, and complex on-site energies, are considered. It is found that topological nonzero modes exist in three cases and the topological phase transition cannot be induced by the nonreciprocal superconducting pairing terms and imaginary on-site potential. However, the system undergoes a topological phase transition when appropriate nonreciprocal hoppings are introduced. Although the introduction of the long-range interaction can suppress the non-Hermitian skin effect, it can remerge under specific parameters when three non-Hermitian factors are considered simultaneously. Our findings provide a thorough understanding of the effect of non-Hermitian parameters in the topology of the non-Hermitian Kitaev chain with the long-range couplings, and extend the understanding of the long-range couplings in non-Hermitian physics.

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• Skin effect
• Topological phases of matter
• Topological superconductors
• 1-dimensional systems
• Non-Hermitian systems
• Lattice models in condensed matter