We have demonstrated that Mg is a controllable acceptor element for p-type GaAsN alloys grown by solid-source molecular-beam epitaxy (MBE), where a hole concentration has been realized up to 1.5 x 10(20) cm(-3) and has been controlled along the vapor pressure curve of Mg using a standard effusion cell. In addition, electrical and luminescence characterizations have been investigated for GaAsN:Mg samples grown by solid-source MBE. The activation energy of Mg for the GaAsN:Mg samples is close to the impurity energy of Mg in GaAs (28 meV). Thus Mg is a very shallow acceptor element for GaAsN alloys. From photoluminescence (PL) measurements, the integrated PL intensity drastically increases with increasing a hole concentration up to 8.6 x 10(19) cm(-3) at 300 K. This result suggests that the hole concentration can increase up to 8.6 x 10(19) cm(-3) without significantly increasing the non-radiative recombination centers related to Mg doping when Mg is the acceptor element. (C) 2009 Elsevier B.V. All rights reserved.