We propose a new depth of interaction (DOI) detector which is made of scintillation crystals cut in triangular prism. Preliminary study was carried out with Lu2xGd2(1-x)SiO5 (LGSO) crystals cut in three-square of 3.0 mm and 10.0 mm long. They are arranged in 3-layer DOI array and coupled to a position sensitive photomultiplier tube (PS-PMT). By removing some reflector from the crystal array to control scintillation light spread, we could obtain the 2-dimensional position histogram in which responses of the crystals in all layers are discriminated with only Anger-type calculation of the PS-PMT signals.2008 Nuclear Science Symposium, Medical Imaging Conferenc