The pizza delivery chain has 1000 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," 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 2500 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.
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.
He said it was not the fault of Bulgarians or Romanians or any other nationality if they were prepared to work hard for less money than Britons.
He said: "There are a lot of people who complain about their lot. Life is tough for everybody at times.
"I know people will look at me and say, 'It's all right for you'. But I started off with pretty well nothing."