Grant was arrested in December 2011 in Mombasa with various chemicals, batteries and switches, which prosecutors say he planned to use to make explosives. He denies the charges.
Today's hearing, the counter-terrorism officer, Detective Inspector Stephen Ball, told the court that Jihadist documents and other materials "clearly dedicated to the making of explosives and weaponry" were found on a flash storage drive allegedly in Grant's possession.
The detective said other document detailed chemicals that could be used to make explosives, and various ways of making booby-traps to target government officials, police or bomb disposal teams.
Prosecutors have accused Grant, a 30-year-old Muslim convert, of working with fellow Briton Samantha Lewthwaite -- the fugitive widow of British suicide bomber Germaine Lindsay, who blew himself up on a London Underground train on July 7, 2005, killing 26 people.
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Lewthwaite, a mother-of-three and daughter of a British soldier, is wanted by Kenyan police and there was some speculation that she was involved in last year's Westgate mall siege in Nairobi.
Reid, who claimed he was an Al-Qaeda recruit, is serving a life sentence in the United States for trying to blow up a flight from Paris to Miami in December 2001.
In December 2011 Grant pleaded guilty to charges of being in the country illegally and lying about his nationality, for which he was sentenced to two jail terms of two years, to run concurrently.