Peter Andrew Milner, 51, pleaded guilty to seven counts relating to sexual activity with a child and rape of a child at Shrewsbury Crown Court.
The offences relate to the same victim between 2007 and 2014.
Mr Ben Lawrence, prosecuting, said: "The pleas are acceptable to the crown."
A further 12 offences were allowed to lie on file at Monday's hearing.
The court heard that Milner, who has links to south Wales, was jailed for 18 years at Swansea Crown Court in 2019 over child sex offences committed between 1995 and 2005. He is a serving prisoner.
Judge Anthony Lowe adjourned the latest case until February 26 when Milner will be sentenced for the Shropshire offences