We carried out the photoluminescence measurements at low temperature for Be-doped GaAs. Samples were grown by molecular beam epitaxy and Be con- centration was varied by controlling the cell temperature of Be. Besides the well-defined emission, [g-g], which is observed for the acceptor con- centration [A] from ∼ 5x1016 cm-3 to ∼ 1x1018 cm-3 and which shows steep red shift with increasing [A], we observed two unusual emissions temporarily denoted by [g-g]α and [g-g]β. These emissions were commonly observed just below bound exciton emissions for heavily-doped region of [A]>1x1018 cm-3. [g-g]α indicated a strong blue shift with increasing [A] and its energy can become larger than the direct band-gap energy of undoped GaAs at 2K when [A] exceeds 5x1019 cm-3. On the other hand, [g-g]β was observed in the vicinity of the band-to-acceptor emission and showed red shift with increas- ing [A]. We here proposed a model that these two emissions are attributed to the binding states of acceptor-acceptor pair formed by the overlapping of the wave functions in the ground state of an isolated acceptor. This situation is principally different from that of [g-g] in which the formation of acceptor-acceptor pair was ascribed to the overlapping of the wave func- tions of 2P excited state. It was revealed that the theoretical estimation made through the simplified calculation agreed qualitatively well with the dependence of [g-g]β on [A]. However this calculation presented unsatisfac- tory agreement with the features of [g-g]α and it was suggested that another physical conjecture such as a formation of GaAs-Be alloy should be proposed.