Bradford Community Health NHS Trust, in partnership with Bradford Hospitals Trust, Shipley College and other city organisations, says it is anxious to have a nursing workforce that more accurately reflects the ethnic diversity of the community.
The scheme has been launched at a time when hospitals are urgently seeking more innovative ways to recruit nurses to meet shortages.
Apprenticeships last two years and participants receive a training allowance and work alongside qualified nurses.
"The scheme is a paid opportunity for individuals to gain real insight into nursing while gaining an academic qualification needed to begin nurse education," said Diana Oliver, project manager.
"It is designed to attract those who would not normally consider nursing as a career.
"It will also address some of the concerns over the links between unemployment and ill-health and the inequality of access to health services for minority ethnic communities."
Ishtiaq Ahmed, the director of Bradford Racial Equality Council, welcomed the idea, saying that the under-representation of ethnic minorities in nursing had long been recognised.
"This scheme offers good quality, real jobs in the NHS," he said.
The minimum qualifications needed to start the scheme are four GCSEs grade A-C. But if candidates have not gained GCSEs they can take an entry test at Shipley College.