We introduce the LUNA neutron detector array developed for the investigation of the 13C(α,n)16O reaction towards its astrophysical -process Gamow peak in the low-background environment of the Laboratori Nazionali del Gran Sasso (LNGS). Eighteen 3He counters are arranged in two different configurations (in a vertical and a horizontal orientation) to optimize neutron detection efficiency, target handling and target cooling over the investigated energy range E keV (E in emitted neutron energy). As a result of the deep underground location, the passive shielding of the setup and active background suppression using pulse shape discrimination, we reached a total background rate of counts/hour. This resulted in an improvement of two orders of magnitude over the state of the art allowing a direct measurement of the 13C(α,n)16O cross-section down to E keV. The absolute neutron detection efficiency of the setup was determined using the 51V(p,n)51Cr reaction and an AmBe radioactive source, and completed with a Geant4 simulation. We determined a (34 ± 3) % and (38 ± 3) % detection efficiency for the vertical and horizontal configurations, respectively, for En=2.4 MeV neutrons.