The arrest comes after electronic items and documents were seized from an address in Brookside Avenue, Coventry, last week.
A number of homes in the area were evacuated after the man was detained under the Explosives Act on 24 April before initially being released.
Searches were carried out at the property by West Midlands Police and the Army’s Explosive Ordnance Disposal (EOD) for several days and concluded at the weekend.
Police said the man was arrested for a second time on Thursday on suspicion of being concerned in the commission, preparation or instigation of acts of terrorism under Section 41 of the Terrorism Act 2000.
He is being detained at a West Midlands police station.
Chief Superintendent Mike O’Hara said: “I would like to thank local people for their co-operation during the searches and apologise for any inconvenience caused.
“This is a complex inquiry that remains subject of a thorough investigation.
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“The searches and evacuations were essential for officers and EOD to enable them to conduct their work and keep local people safe.”
No further police activity is taking place at the property, the force said.