Sky News reported that Khalid Khaliq of Leeds was released by City of Westminster magistrates in London until a July 2 court date.
Khaliq, 34, faces a maximum 10-year prison term. He has denied the charge, which was brought under the Terrorism Act 2000.
Police said Khaliq possessed "a document or record namely the al-Qaida training manual containing information of a kind likely to be useful to a person committing or preparing an act of terrorism," Sky News reported.
He was arrested by police investigating the July 7, 2005, London bombings that killed 52 people.
Meanwhile, Hasina Patel, whose husband was the ringleader in the 2005 bombings was released without charge, as were her brother, Arshad Patel, and another man, Imran Motala, Sky News reported.