The parents and brother of Dean McIwaine, from Newtownabbey, were speaking at a police news conference.
The PSNI has carried out extensive searches for the 22-year-old barber and have also appealed for him to make contact with them.
Mr McIwaine was last seen in the Carnmoney Road area of Newtownabbey on Thursday, 13 July.
His father, Rod, said the family was distraught and lost without him.
His mother Karen spoke of her disbelief that her son was missing and said that she just wanted him to come home.
His brother Glenn said: "It's not like him, he would always be in contact, he would always text me... ring somebody.
"He needs to come home now.
"He was opening his barber's at the end of this month, he had everything going for him.
"I wish he would realise that and come home to see us," he added.
On Wednesday, police searching for Mr McIlwaine released CCTV footage taken on the day he went missing, it is understood that he was at a barbeque with his family and friends the day before.
At that time, officers also revised details of what they believe he was wearing on the day of his disappearance.
Det Insp Chris Millar said: "It has now been established that Dean was wearing a short-sleeve maroon shirt, denim knee-length shorts and dark-coloured canvas shoes.
"He was wearing a gold watch on his right wrist."
Mr McIlwaine is 5'8" in height and of medium build.
He has dark hair, a beard and sleeve tattoos on both arms.
Anyone with information on his whereabouts is asked to contact police by calling 101, quoting reference number 121 of 14/7/17.
The family of a missing County Antrim man who was last seen a week ago have pleaded for him to come home.