Helen Bailey's body was found by her father in woodland near the M6 on 11 August 1975 after she never returned from playing out the previous afternoon.
Dressed all in blue when she died, Helen became known as Little Girl Blue.
The case has been highlighted by the BBC's Crimewatch Roadshow.
Det Supt Caroline Marsh said: "This is a direct appeal to the offender or anyone who may have spoken to the offender about what happened that day."
See more stories from Birmingham and the Black Country here
Helen was playing at the park near her home on Booths Farm Road in Perry Barr on 10 August 1975 when she returned home at about 14:30 BST in a "dirty state", Det Supt Marsh told BBC Crimewatch.
She went out to play again after her mother washed and redressed her but did not return at tea-time.
Her parents went out to look for her and alerted the police when they couldn't find her.
Officers conducted an overnight search involving members of the public and Helen's body was found the following morning with her throat cut in woodland near the M6.
Helen's mother, Margaret Bailey, said: "It's with me all the time and I just want closure. I'd like to think I can finish my life knowing justice has been done for Helen."
Helen would have celebrated her 50th birthday in May.
"I just wonder what she would have been. She would have been engaged perhaps, got married and had a family. And we've been robbed of all that," Ms Bailey added.
Det Supt Marsh, who is investigating the case, said police "strongly believe that the person responsible for Helen's murder has confided in someone" and are appealing for them to come forward.
A fresh appeal has been made into the murder of an eight-year-old girl in Birmingham 42 years ago.