The 41-year-old, of Whaddon Road, has been abused in the street and had his home vandalised by gangs.
In the latest attack, thugs hurled stones at the house, smashing the glass of the front door.
Roby said the family was petrified as the gang of youths peppered their home with stones and eggs, kicking at the door in a prolonged onslaught.
"It was really nasty," he said. "I wasn't there at the time so my wife and children were at home on their own.
"Just imagine how they felt. They were terrified."
The father-of-two, who is originally from India, said the incident is the latest in a string of racist attacks since his family moved to Cheltenham five years ago.
"It has been going on for some time and it seems to be getting worse," he said. "This is the fifth time I have had to repair a window at my home because of something like this.
"I have had to put up with teenagers shouting abuse from the park opposite.
"It makes me sad. The whole family has been made to feel unhappy."
Roby, who grew up in southern India, came to the UK in 2005 after his wife Smitha got a job working as a nurse for the NHS.
He found work as an architectural technician and the couple sent their son, five, and daughter, 10, to a local school.
"We came here to work and to bring our children up in a safe environment," he added.
"I accept the people responsible for this are in a minority, but it has become a problem.
"Nobody should have to put up with this sort of abuse. It has to stop."
Gloucestershire police said they were aware of ongoing problems and were intent on bringing a stop to the anti-social behaviour.
Inspector Roddy Gosden, of Whaddon Safer Community Team, said: "We fully support the Mekkara family and are taking reports of the latest incident very seriously.
"We are aware there have been problems in the past and a lot of work has gone into investigating them – including putting up CCTV cameras at the house to identify who is responsible.
"This kind of behaviour will not be tolerated in our community. We are stepping up our efforts to bring these problems to an end for the Mekkaras and appeal for anyone with information to get in touch."
A year ago Sri Lankan national Suda John said attitudes towards ethnic minorities in Cheltenham were worse than ever.
The 31-year-old, from Lansdown, said the situation had got so bad he was considering leaving the town that has been his home for the past six years.
He said: "I've been abused on the street, outside my home and even at work.
"If it happens once you think it might be just one idiot, but when it keeps happening you think there must be a deeper problem."
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