Officials said at least 54 people were wounded.
"First the father [Bashir Bilour] was killed, now the son has been targeted", said Wali adding that they are targeting Bilour family, because they know that as long as the family is there no one can take over the city of Peshawar. His father Bashir Bilour, also a prominent politician, was killed by a suicide bomber in 2012.
A foreign news agency cited a police officer, Iqbal Khan, as saying that the bomber struck a Tuesday night rally for ANP candidate Haroon Ahmed Bilour.
Police, security forces and rescue teams rushed to the site and transported the injured to hospital. Some people were seen crying.
Meanwhile, the responsibility for the Peshawar suicide blast has been claimed by the Pakistan faction of outlawed Tehreek-e-Taliban.
But many militants have escaped into neighbouring Afghanistan, from where Islamabad says they launch attacks back into Pakistan.
Haroon Bilour, who was set to contest the July 25 elections from Peshawar's PK-78 constituency, will be buried in Wazir Bagh at 5pm today (Wednesday).
"I lost consciousness after the blast".
Another party worker, Yaseen Khan, said a deafening explosion rocked the compound as Haroon Bilour shook hands with supporters. This is the second attack before Pakistan's assembly elections.
Major General Asif Ghafoor, an army spokesman, said 371,388 troops - almost a third of the total armed forces - would be deployed to provide security for the upcoming vote.
But ANP leaders have vowed to continue their campaign this year despite the bombing in Peshawar.
Responding to a question about the deadly attack on the party leader, "These are terrorists we are dealing with".
"Political differences apart, all political parties and their candidates must be provided proper security during their election campaigns by the state", he said in a tweet.
Global and Pakistani rights groups have recently accused the army and its intelligence agency of intimidating media outlets in an attempt to stifle criticism of the military, accused by some of seeking to play a dominant role in the country's politics.