A homemade pipe-bomb was pushed through the letter-box of a house in Salford while a family slept upstairs.
The device exploded, damaging the front door of the house on Westminster Street, Swinton, and blowing the letter-box off.
A 61-year-old man and his wife, 38, were upstairs along with their son, 20, and daughter, 12, when the house was targeted last Saturday.
Anyone with information is urged to contact police.
The son heard footsteps outside the house and saw a man at the bottom of the garden at about 2345 BST.
He then saw a bright flash outside followed by a loud explosion that caused the house to shake.
When the family went outside they found a haze of blue smoke.
Police found the device was a homemade pipe-bomb. Ball-bearings and shrapnel were recovered from the scene.
The man was described as white, about 5ft 4in tall and slim. He was wearing light blue jeans and a black hooded top pulled over his face.
Det Con Andrew Quinn said: "At this stage we do not know why this family were targeted in such a way but our paramount concern is to find this dangerous offender and lock him up.
"The family deserve the peace of mind of at least seeing this man behind bars so please, if you have any information whatsoever, do call us."