About 40 women have joined the network and staged topless protests in at least three cities, said Sanna Ferm, 22, one of the founders of the group called Bara Brost, or Bare Breasts.
"The purpose of the campaign is to start a debate about why women's bodies are sexualized," Ferm said Wednesday.
She said the fact that men can be bare-chested in public swimming pools but not women is "a concrete example of how women have fewer rights than men."
Reactions from other swimmers have ranged from support and encouragement to anger and even indifference, she said.
The network was formed after two women who were swimming topless in a public swimming pool in Uppsala, north of Stockholm, were asked to cover up or leave.
Women can sunbathe topless in the summertime at beaches around Sweden, which is known for its relaxed attitude toward nudity, but they are required to wear tops at public swimming pools.
Inger Groteblad, a manager at the swimming facility in Uppsala, said it was a matter of security.
"We want to make sure that girls don't get subjected to sexual harassment," she was quoted as saying by tabloid Aftonbladet.
The women have filed a complaint against the facility to Sweden's Equal Opportunities Ombudsman.