"The bomber drove the car into the gates of the police headquarters in Jalalabad city," Ahmad Zia Abdulzai, spokesman for the Nangarhar provincial governor, told AFP.
"We have two policemen martyred, eight others including a traffic officer were wounded in the attack and they have been taken to the hospital. The bomber is dead."
Jalalabad, the capital of Nangarhar province, straddles the main route from Kabul to Pakistan's tribal belt - a hub for Taliban and al Qaeda-linked militants.
The city has seen a series of attacks in the past year.
In August, suicide bombers targeted the Indian consulate, detonating a car bomb and killing nine civilians, including seven children in a nearby mosque.
There was no immediate claim of responsibility for Saturday's attack, which came as President Hamid Karzai and Kerry held a second day of talks in Kabul.
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pakistan should stop barbaric terrorist attack.
peace full activities of people of peaceful religion.
more peacefulness from the followers of religion of peace.