Medway Council initially proposed closing all 19 of its Sure Start centres and replacing them with four larger hubs.
But a public consultation showed 85% of respondents were against the plans.
Now the council has agreed to keep 13 centres open, four of which will become children and family hubs.
After the cabinet meeting on Tuesday afternoon, the council tweeted its decision: "Cabinet has approved item 4's recommendations, incl the option to establish 4 Family & Children Hubs & 9 Children & Family Wellbeing Centres."
Council leader Alan Jarrett said the changes were necessary as the budget for the centres had been "haemorrhaging money" since they were first set up.
Councillor Andrew Mackness, Conservative lead member for children's services, added that it had been a "difficult decision" but the plans would still deliver "a high-quality service".
After the vote, Medway Labour leader Vince Maple tweeted: "Remember 94% of respondents did not support the Hub & Satellite proposals yet Tory @medway_council presses ahead anyway. #SaveOurSureStart"
And campaign group Save Sure Start Children's Centres in Medway tweeted: "Always remember: You can never trust the @Conservatives. Years of lies from Tory MPs about safeguarding Sure Start."
The sounds of children crying aren't what you usually get at a council meeting.
But this afternoon cabinet at Medway Council was packed with concerned parents and their little ones.
They'd been protesting outside against plans to close six out of 19 Sure Start centres.
After cabinet voted through proposals they were greeted with shouts of "shame".
Despite the council changing its original plans to close all 19 and replace them with four larger hubs, the parents I spoke to weren't convinced the service would stay the same.
Even though the decision has been made campaigners say they'll keep fighting.
The council said it hoped to save Â£1.6m as a result of the changes.
Councillors have voted in favour of shutting six Sure Start children's centres amid heckling from a packed public gallery.