"The Asiatic lion is one of the most critically endangered species on this planet and this added twist of so many lions being killed by electrocution... is a catastrophe", said Belinda Wright, the society's executive director.
"Preliminary information suggests that the three lionesses and two cubs were electrocuted by a crop protection fence put up by a farmer near Dhari, Amreli district, in an area adjoining Gir National Park," she said in a statement.
"This new tragedy brings the number of Gir lions that have died this year to a staggering total of 32 lions."
The society listed eight lions killed by poaching, six electrocuted, five fallen into wells, one hit by a vehicle and 12 others found dead.
The Wildlife Protection Society of India is already working closely with the enforcement authorities to curb the killing of lions by professional poachers, the society said.
The number of Asiatic lions plummeted from around 1,000 a century ago to just 20 in 1913 but the creation of the Gir sanctuary after India's independence from British colonial rule in 1947 helped revive the population.