The spin-polarized annihilation lifetime of a positron (SPALP) trapped by the Ga vacancies in GaN was investigated using two-component density functional theory calculations with geometry optimization. SPALP clearly depends on the charged states of the Ga vacancies and the induced magnetization. This dependence is attributed to the overlap between the positron and electron densities around the defect. Thus, the present study proves the useful role of SPALP for probing and revealing the mechanism of d(0) ferromagnetism. (C) 2016 The Japan Society of Applied Physics