The magnetic phase diagram of a diluted three-dimensional Ising antiferromagnet Ni_cMg_1-c(OH)₂ is determined. It consists of a spin-glass phase for 0.1 < c < 0.5, a re-entrant spin-glass phase for 0.5 ≤ c ≤ 0.8 and an antiferromagnetic phase for 0.5 ≤ c ≤ 1. The dynamic aspect of the spin-glass phase and the re-entrant spin-glass phase is studied from the temperature, frequency and field dependence of dispersion χ´ and χ´´. The relaxation time for c = 0.25 and 0.8 diverges in accordance with a critical slowing down with a dynamic critical exponent x = 8.79 ± 2.44 for c = 0.25 and 10.1 ± 1.3 for c = 0.8. The re-entrant spin-glass phase at c = 0.5 and 0.6 may be a mixed phase of spin-glass phase and antiferromagnetic phase. The competition between ferromagnetic intraplanar and antiferromagnetic interplanar exchange interaction gives rise to spin-glass behaviour.