SP Manweb is set to put up 18 pylons linking two wind farms in Clocaenog Forest with a substation at Glascoed, near St Asaph.
The plans were approved by Energy Secretary Greg Clark last year.
Opponents argued it would impact the countryside and farming, and called for the cables to be laid underground.
The judicial review focused on the impact the scheme would have on a Grade II-listed farm complex at Berain, near Llannefydd, which was home to Katheryn of Berain, a descendant of Henry VII.
But the presiding judge, Mr Justice Lewis, ruled that Mr Clark had applied the relevant policies when deciding whether to give the application the go ahead.
A legal challenge to try and stop overhead cables being erected across parts of rural Conwy and Denbighshire has been dismissed by the High Court.