In July, UK Energy Secretary Greg Clark approved SP Manweb's proposal for 17km (10.5 miles) of power lines linking Clocaenog wind farm to a substation at Glascoed.
This followed a public inquiry into the plans last year.
SP Manweb said the decision to have a review does not change their programme.
The High Court hearing will take place in Llangefni in April.
The Pylon the Pressure group are campaigning for the cables, which will carry supplies from four windfarms in the Clocaenog and Brenig areas, to be laid underground.
The group's chairman, Dyfrig Hughes, said the scheme will "blight one of the most beautiful and historic landscapes of north Wales".
He added: "Unfortunately for us, the UK government agreed with them [SP Manweb] and granted permission despite underground cabling costing no more than overhead lines over the lifetime of the connection."
During the inquiry, then UK Energy Secretary Ed Davey said the additional Â£16m cost to lay the cables underground would be disproportionate.
Campaigners also had concerns the pylons would spoil a 16th-Century farmhouse near Llannefydd.
But the examination authority has said the visual impact on the building over the power lines' 30-year lifetime would be minimal.
A spokesperson for SP Energy Networks said: "We are aware of the judicial review, and we will monitor developments and continue to work closely with our clients.
"This decision does not impact on our programme, and work to develop our plans will continue.
"The decision to approve our proposals to connect two new wind farms in north Wales followed four years of detailed planning and consultation."
Opponents of an overhead cables scheme across parts of rural Denbighshire and Conwy have won the right to a judicial review.