It would supply power through undersea cables to Chàm Island in the central province of Quảng Nam possibly from September, EVN said.
In the Cửu Long (Mekong) Delta province of Kiên Giang, Lại Sơn Island is expected to be linked by the end of this month.
Work to supply electricity to Hòn Nghệ Island Commune in Kiên Giang is 25 per cent complete and likely to be finished this quarter.
In the north, Cái Chiên Island Commune in Quảng Ninh Province, the only island not to have power the province, will be linked soon.
From now through 2020 EVN will focus on wrapping up a 2013-20 programme to supply power to all rural and mountainous areas and islands.
In May an EVN team did a survey on solar and wind energy generation in the Trường Sa (Spratly) archipelago, and found that 33 had power supply.
EVN will seek Government permission to supply electricity to all islands in Trường Sa (Spratly), according to Phạm Minh Thắng, an EVN board member.
In the first six months of the year EVN supplied 76.44 billion kWh of electricity, a 11.7 per cent increase year-on-year.
During the period demand was up 10.3 per cent in the central region, 11.96 per cent in the north and 12.28 per cent in the south.
Despite the rapid rise in demand, EVN has assured it can continue to meet it.