Details of the background, that is, “unwanted signals accumulated by the data acquisition system of neutron instruments,” observed by the cold-neutron chopper spectrometer AMATERAS installed at the Materials and Life Science Experimental Facility at J-PARC are reported. In the design phase of AMATERAS, we carefully considered the achievement of high signal-to-noise ratio, and possible countermeasures were implemented. Actually, recent scientific outputs from AMATERAS indicates that the spectrometer is one of excellent neutron instruments with low background. In spite of that, in nine years of AMATERAS operation, we have encountered unwanted signals due to various reasons, including γ rays emitted at materials on or near the beam line including the sample itself, scattered neutrons from the beam line devices, air scattering, electronic noise in data acquisition system, cosmic rays, T0 burst, and other unknown sources. In this report, we discuss the background observed by AMATERAS, especially in the conditions of without samples, comprehensively. The possible sources of these signals and the countermeasures considered against the above sources are discussed, which may be helpful to those who are engaged in other existing or planned neutron-scattering instruments.