Shelter says one in 10 renting families in England has had to change their children's school due to a move.
Government figures show 3.8 million households in England were living in the private rented sector in 2011-12 - 17% of the total.
The National Landlords Association said it backed the call for stability.
In a survey of 4,327 adults living in the private-rental sector in England, Shelter found 44% thought their children would have a better childhood if they had more stability in their housing arrangements.
Less than 10% of those surveyed valued the freedom and flexibility renting gave them.
And 28% said their landlord or letting agent had failed to carry out repairs or deal with poor conditions in the past year.
The poll found nearly two-thirds of renting families (64%) would like to own their own home but do not think they will ever be able to afford it, and 43% expect to be living in rented accommodation for the next 10 years.
Shelter says a generation of children is growing up in "unstable, unaffordable, poor quality homes".'Constant upheaval'
The charity wants to see the introduction of a "stable rental contract" to give renters a better deal.
The contract would give renters five years in their home during which they could not be evicted without good reason and would have a guarantee the rent would rise by no more than inflation.
It would give renters the chance to decorate their homes and allow them to end the contract with two months' notice, while giving landlords the right to end the tenancy if they sold the property.
Currently, tenants have the right to live in a property that is safe and in good repair, live in the property undisturbed and be protected from unfair eviction and unfair rent.
Tenants also have the right to challenge excessively high charges and to have their deposit returned when the tenancy ends.
Chief executive Campbell Robb said: "For the vast majority of renting parents, renting isn't a lifestyle choice, yet for many it's putting their children's education, happiness and wellbeing in jeopardy.
"Unpredictable rents and short-term tenancies are not only failing to meet the needs of families, they're doing real damage to children's lives.
"No child should have to deal with constant upheaval, a disrupted education and an atmosphere where parents are constantly worried about paying the rent or having to find somewhere new to live.
"Making tenancy contracts more stable could improve the lives of children across the country by giving families more stability in their homes, and would give landlords a more predictable income.
"The nine million renters in this country deserve better. It's high time we faced up to the fact that renting is no longer a stepping stone, but the only long-term option available to rising numbers of families."'Fair private sector'
Chris Norris, head of policy at the National Landlords Association, said: "The NLA supports a fair and balanced private-rented sector which meets the needs of tenants and we support Shelter's call for stability in the home.
"Whilst the private-rented sector must provide the stability associated with home ownership, it is also important that landlords and tenants are able to negotiate terms that suit both parties.
"It is essential that landlords receive a level of rent to cover their business costs and we advise landlords to only increase costs between tenancies to ensure their rents are in line with market rates.
"At the NLA we promote professional standards and encourage all landlords to sustain good quality, enduring tenancies."
A spokesman for Department for Communities and Local Government said: "There is no legal barrier to long-term tenancies. "However, restrictive laws making this compulsory would mean fewer homes to rent, less choice and higher rents.
"With 75% of tenants moving out of choice, and only nine per cent of tenancies ended by the landlord, we are determined to do all we can to help tenants and landlords get a fair deal in a way that doesn't jeopardise that flexibility or strangle the industry in red tape."