Denis Bradley said he would not be driven off the board by the attack, which followed threats from dissident republicans in the Real IRA last year.
Mr Bradley's wife and teenage son were at the family home in Templemore Park in the Rosemount area of Derry when it was attacked shortly before 9pm on Thursday.
However, no one was injured as one of the petrol bombs detonated inside the porch and another failed to explode.
The attack was condemned as cowardly by Northern Ireland Security Minister Jane Kennedy and Policing Board chairman Professor Desmond Rea.
Police chiefs and Sinn Féin added their voices to the condemnation of the latest in a series of attacks on people associated with the new policing structures in Northern Ireland.
Mr Bradley was not at home when the attack took place he was in Belfast meeting victims of a growing tide of racist attacks on ethnic communities in the city. Insisting he would not be forced into quitting his important post, he said: "I won't be leaving any Policing Board, I won't be leaving anything.
"It was two children who did this to me some adult sent them out there was no real damage."
But he warned that if such attacks continued someone would eventually be killed.
"There will be deaths some day, someone will be killed, someone will be hurt."
The local policing commander, Chief Superintendent Richard Russell, said that, while the damage was minimal, the consequences of the attack could have been disastrous.
"We could have been looking at a double fatality here.
"It is scandalous to attack a house with a woman and young boy inside, the potential consequences could have been disastrous."
Mr Bradley, a former Catholic priest, served as a go-between in secret talks between the British Government and the Provisional IRA during the Troubles.
Professor Rea described the petrol-bombing as an "act of wanton cowardice". Sinn Féin's Mitchel McLaughlin branded those responsible for the attack as "mindless idiots".