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Abstract In this paper, a non-selective harvesting Lotka–Volterra amensalism discrete model incorporating partial closure for the populations is proposed and studied. By applying the relevant conclusions of difference inequality and some calculation technique, sufficient conditions are obtained to ensure the permanence and extinction of the system. By constructing a suitable Lyapunov function, sufficient conditions that ensure the global attractivity of the system are obtained. Finally, numerical simulations show the feasibility of our results.