A Home Office scheme offering 10,000 Bangladeshis year-long work visas to take up unskilled jobs in the UK has been criticised by Migrationwatch.
Sir Andrew said the Home Office scheme was "incomprehensible"
The think-tank said it "defied logic" because the 2001 census showed there were 10,000 unemployed 16-24 men who identified themselves as Bangladeshi.
Migrationwatch's Sir Andrew Green said people already here should be offered these jobs or be trained to do them.
The Home Office said the visas were for jobs which could not be filled.
The work permits were only offered for jobs which employers had clearly demonstrated that they could not fill after a long period of advertisement, a Home Office spokesman said.
The numbers of permits offered is decided after officials sit down with the different sectors of industry, he added.
Under the sector-based scheme, unskilled workers from other countries are allowed in to Britain for up to a year to fill vacancies in industries with job shortages such as agriculture and hospitality.
"The number of low-skilled workers allowed into the UK from outside the EU remains small compared with other countries and is controlled by strict quotas which have been further reduced since EU accession (in May)," the Home Office said.
But Sir Andrew said: "It is incomprehensible that when there are large numbers of young Bangladeshis already here who are unemployed it should be thought necessary to issue work permits to many thousands more.
"Surely the people already here should be offered these jobs, or should be trained to do them, before we add still further to immigration. It simply defies
According to independent agency the Immigration Advisory Service (IAS) last year's entire Bangladeshi quota was used up within several weeks - mostly by employers from Britain's curry houses.
It has now been closed.
The vast majority of applicants are now being refused entry, many because officials believe they will outstay their visas.
Ashraf Uddin, secretary general of the Bangladesh Caterers Association, is appealing to the Home Office for urgent talks, because his organisation believes 20,000 more people are needed.
Some restaurant owners spoken to by the BBC say taking on the long-term unemployed has been difficult in the past - not least if the individuals have problems such as drug abuse or no experience of working the long hours the business demands.
The Joint Council for the Welfare of Immigrants policy director Tauhid Pasha said: "Andrew Green overlooks the fact that many young men of Bangladeshi descent were born and educated in this country and one of the reasons they are not filling vacancies in the hospitality trade may be that they have different career ambitions.
"Some of them might aspire to be diplomats or barristers.
"On his simplistic view he might as well say that because too many northerners are unemployed in London no more northerners should be allowed to move to London."