Alzheimer's Disease International says 44 million people live with the disease, but that figure will increase to 135 million by 2050.
The figures were released ahead of the G8 dementia summit in London next week.
In the UK, dementia research receives one eighth of the amount of funding that is spent on cancer, which charities say is insufficient.
Alzheimer's Disease International expects increasing life expectancies to drive a surge in cases in poor and middle-income countries, particularly in South East Asia and Africa.
Currently 38% of cases are in rich countries. But that balance is predicted shift significantly by 2050, with 71% of patients being in poor and middle-income countries.
The report says most governments are "woefully unprepared for the dementia epidemic".
Marc Wortmann, the executive director at Alzheimer Disease International, said: "It's a global epidemic and it is only getting worse - if we look into the future the numbers of elderly people will rise dramatically."
Jeremy Hughes, chief executive of the UK's Alzheimer's Society, said: "Dementia is fast becoming the biggest health and social care challenge of this generation.
"We must tackle dementia now, for those currently living with the condition across the world and for those millions who will develop dementia in the future.
"The G8 is our once-in-a-generation chance to conquer this condition and we must see meaningful action after the talking is over."
Rebecca Wood, the chief executive of Alzheimer's Research UK, said: "Increasing numbers of people affected by dementia worldwide is cause for alarm, but research can stem the tide.
"An intervention to delay the onset of Alzheimer's by five years could halve the number of people who die with the disease, having a transformative impact on millions of people's lives.
"This progress can only come through research and these figures are a timely reminder of the scale of the challenge ahead of the G8 dementia research summit."
The number of people living with dementia worldwide is set to treble by 2050, according to a new analysis.