"While the population growth of cities in the industrialised world has somewhat stabilised, most of the increase occurs in the cities of the poor, less developed nations", the institute says.
Bombay, home to about 18 million people, will over the next two decades see its population grow to about 28.5 million, according to the Washington-based Population Institute, in its annual overview of world population trends.
And India will have three cities in the list of the world's top 10 most populous cities, according to the institute's projections - with Calcutta and Delhi in ninth and tenth places.
New York and Los Angeles will have dropped out of the top 10, ousted by Dhaka and Karachi.
Rapid growth
In 1900 the world's most populous cities were all in North America and Europe. But at the end of the century, Tokyo, New York and Los Angeles were the only industrialised cities to feature on the list of the 19 cities which have populations of at least 10 million people.
"While the population growth of cities in the industrialised world has somewhat stabilised, most of the increase occurs in the cities of the poor, less developed nations", the institute says.
Six of every 10 children in the developing world are projected to live in cities by 2025, and more than half of them will be poor.
At present, 47% of the world's six billion population lives in cities and more will join them. That will put pressure on governments to make urban areas better places to live.
While the main attraction of cities is opportunity, their rapid growth leads to pressures on infrastructures, manifested in sanitary, health and crime problems, the report says.
Unskilled people arriving from rural areas frequently end up performing menial jobs at low wages or resorting to begging and stealing, it adds.
Urban pressure
Most of the population increase will take place in the world's poorer countries. But even in wealthier countries, more and more educated people will move from rural areas to cities in search of better opportunities.
"By 2050, an estimated two-thirds of the world's population will live in urban areas, imposing even more pressure on the space infrastructure and resources of cities, leading to social disintegration and horrific urban poverty," says Werner Fornos, president of the Washington-based institute.
The Population Institute is an independent, non-profit organisation, established in 1969. It has members in 172 countries and receives funding from foundations, corporations and individuals.