Police officials said 12 civilians and five police officers were also wounded in Saturday’s attack.
"A remote-controlled bomb exploded as a police van carrying four prisoners passed by an abandoned tin of vegetable oil in Peshawar city on Saturday, killing one policeman and wounding 17 others," local police official Mohammed Asif said.
A woman and four policemen were among those wounded.
Another local police official, Javed Iqbal, also confirmed the incident and casualties.
No group has claimed responsibility, but the Taliban often targets police, military troops and other security forces.
A taxi driver was killed when a mortar bomb hit his cab in the upmarket Hayatabad area of Peshawar on Friday night, police official Tahir Ayub said.
Ayub said the headquarters of the paramilitary Frontier Constabulary in the area was apparently the target of the mortar bombs fired from the neighbouring Khyber tribal region.
"However, three mortars landed in open spaces while three others hit a house, a taxi cab and a shop," he said, adding that at least four people were wounded in the attack.
According to agencies report, around 5,000 people have been killed in militant attacks across the country since July 2007.
There were about 120 bomb attacks in Pakistan in 2011, up on the 96 bomb blasts in 2010, but far lower than violence in 2009 when there were 203 bombings across the country.