The pizza delivery chain has 1,000 jobs, including as drivers and cooks, which are unfilled, said Lance Batchelor.
"We're struggling to get enough employees. Since the immigration laws were tightened up two or three years ago, we are finding it harder and harder to hire staff, especially in London and the South East," he said.
"People who would have worked here a few years ago now don't want these jobs. We could fill 1,000 jobs across the UK tomorrow if we could get candidates to apply for them."
Domino's employs 25,000 people in the UK and every year opens 45 new branches - creating 2,500 new jobs.
The industry could be helped by the relaxing of rules on migrants from Bulgaria and Romania crossing the border from January 1, he argued, saying the Government should introduce a properly vetted system to help bring staff from outside the UK to work at companies like Domino's, rather than potential workers having to have a PHD to do so.
Mr Batchelor said Domino's employs 25,000 people in the UK and every year opens 45 new branches - creating 2,500 new jobs.
Sir Stuart Rose, the former Marks and Spencer chief executive, has defended immigrants who come to Britain and are prepared to work for lower wages.
Mr Batchelor, who is set to leave Domino's in April, added: "Every branch in London is currently operating at less than full capacity because of the problem securing labour. In London it's particularly difficult to get drivers and people to work in production."