Some 28% of 4,818 UK adults questioned by YouGov said they would expect to be turned down if they applied in the next two years.
Many under 25 and over 55 believed their age would count them out, while others cited their living arrangement as the reason they feared they would be turned down.
Fostering Network chief executive Robert Tapsfield said: "It doesn't matter if you are single or living as a couple, how old you are, or whether you have children, a job or own your own house.
"What matters is that you have the skills and experience to look after children separated from their own families, who have often been abused or neglected."
The Fostering Network estimates 8,600 families are needed this year alone, particularly to look after teenagers and children with disabilities.