They want the target for all children to be at least five A*-C grades.
Currently, the target for those in care is just one good grade GCSE. More than half of children in care leave school with none, while less than 1 per cent make it to university.
George McNamara, policy officer at NCH, said: "We think the separate target is totally wrong. It sends a worrying message to teachers and to young people. Youngsters in care come from different backgrounds and have different abilities, just like any other children. Some have the ability to get more than five good GCSEs."
Pam Hibbert, policy officer at Barnardo's, said setting low targets gave the wrong impression of children in care. "If adults expect them not to do as well, it knocks the confidence and self-esteem of the young people.
"What incentive is there for schools and professionals to work harder to make sure these children achieve as much as others?"
Maxine Wrigley, co-ordinator of A National Voice, a charity staffed and run by people who have experienced the care system, joined calls to scrap the separate target. She said more one-to-one tuition for looked-after children could help improve results.
"We should be careful not to assume that everyone is academic," she said.
"Young people should feel at ease about having vocational qualifications instead."
John Bangs, head of education for the National Union of Teachers, said he thought all national targets and performance tables were fundamentally flawed.
"It would be far better to do away with all targets and tables, and concentrate on high expectations," he said. "All targets do is pigeonhole people."
Alex Sykes, who grew up in care, more than met the Government's target by achieving a C grade in double science, which counts as two GCSEs. However, that was his only success - until now. He is now in his final year of a media and public relations degree at Huddersfield university.
"I don't think the teachers expected a lot from me," he said. "To be honest, everyone was more concerned about me surviving every day."
Mr Sykes said he had no one to motivate him to work for his GCSEs and spent much of Year 11 working in a hotel.
A spokesman for the DfES said the department aimed to narrow the achievement gap by reducing the number of times looked-after children were moved from one placement to another.