The Daily Telegraph said that 20-year-old Mohammed Abushamma admitted to trying to travel to Afghanistan in an attempt to join up with the Islamic militant group in its fight against coalition troops.
Abushamma was arrested in April, along with 20-year-old Qasim Abukar, as the pair returned from Turkey.
The two men were thought to have been returning from a failed attempt to travel to Afghanistan to aid the terrorist group.
Abushamma entered his plea in Central Criminal Court following plea negotiations with the prosecution, prosecutor Alison Morgan said.
The student's attorney, Imran Khan, told the court his client is merely a student and asked that his conditional bail be maintained.
"He is now studying at university and is doing well," Khan said.
The Telegraph said while Abushamma has pleaded guilty in the terror case, Abukar has pleaded not guilty to identical charges.