Misassignment of neutron position (ghosting) produces artifacts, which have been observed in wavelength-shifting (WLS) fiber detectors developed for time-of-flight (TOF) neutron powder diffraction. In position-sensitive detectors (PSDs) with WLS fiber encoding, thermal and cold neutrons interact with a monolithic 6LiF/ZnS:Ag scintillator screen, and scintillation photons are generated and transported through the crossed fibers to photomultipliers (PMTs). The neutron position is determined by photon counts in PMTs within a preset time window. Ghosting occurs when neutrons hit the group boundaries of two neighboring PMTs for x-position multiplexing, which is modeled as resulting from a long travel length (about 3-5 mm) of a small number of scintillation photons. This model is supported by the change observed in aperture images when the threshold number for photon-pulses was adjusted for a neutron event determination. When the threshold number of photon-pulses was set above 10 for each PMT, the ghost peaks in the aperture images and TOF spectra of powder diffraction were strongly suppressed or completely eliminated, and the intrinsic background levels of the WLS detectors were significantly reduced. Our result indicates that WLS fiber detector is a promising alternative for 3He PSDs for neutron scattering.