The building is located in a highly secure area The building was close to Pakistani army facilities and the US consulate.
Pakistani Taliban said they carried out the attack, the fourth since Osama Bin Laden was killed on 2 May.
The deadliest attack was a twin suicide bombing which killed more than 80 people, most of them paramilitary recruits, in the north-west two weeks ago.
Last week, the Pakistani Taliban bombed a US consulate convoy in Peshawar, killing one Pakistani passer-by and wounding 10 others.
'Huge blast' Police said the target of the latest attack was the building that housed the police's criminal investigation department.
"It was a huge blast which completely destroyed the three-storey building," AFP news agency quoted Liaqat Ali Khan, chief of police in Peshawar, as saying.
The building is in Peshawar's cantonment area close to the US consulate. Security is usually tight there.
A spokesman for Pakistan's Taliban said the attacks would continue until the US drone strikes and Pakistani military operations were stopped in the tribal regions bordering Afghanistan.
"We will further step up these attacks to avenge Osama Bin Laden's martyrdom," AFP quoted Ehsanullah Ehsan as saying.
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