Muslim Khalid Khaliq, 34, from Beeston, Leeds, admitted to Leeds Crown Court that he owned a copy of the training manual on CD. Police had found the banned work in a raid on his home in the summer of 2005.
A further count of possessing a document or record containing information likely to be useful to a person committing or preparing an act of terrorism was ordered to be laid on file.
Judge James Stewart QC however ordered Khaliq to be found not guilty of a third similar offence.
Sentencing will take place on Tuesday morning. The offence carries a maximum ten-year jail term.
The charges were brought under the Terrorism Act 2000.
Khaliq was one of four people, including the widow of July 7 suicide bomber Mohammed Sidique Khan, who were arrested on May 9 by anti-terror officers.
A police spokesman said he was charged with possessing "a document or record, namely the al-Qa'eda training manual, containing information of a kind likely to be useful to a person committing or preparing an act of terrorism".
He had previously denied the charge and been released on bail by City of Westminster Magistrates Court in central London.



