A new two-dimensional angular correlation of annihilation radiation apparatus is described. Position-sensitive photomultiplier tubes coupled with two-dimensional arrays of small BGO scintillator blocks make simple and compact position-sensitive γ-ray detectors. With a sample-detector distance of 5 m, an angular resolution of 1.1 mrad FWHM and a coincidence count rate of ∼2.4 cps per mCi are obtained. Its performance is demonstrated by the result of a test measurement for KI crystal in which non-localized positronium exists at low temperatures.