The authority has written to all 104 of the borough's schools asking heads and deputies if they want to study for a masters degree in business administration.
The part-time two-year course at Hull University's International Leadership Centre will cost pound;5,000 per person - part of this will come from the staff but most will come from the authority.
The local education authority hopes that the course will enable headteachers to become better leaders and help promote the city to potential job applicants.
"We want the best possible people to come to Hull and, while we don't have a problem filling headships and deputy headships, we do want to improve the qualityof the people applying," said a spokesman.
"We are hoping that by offering headteachers the chance within a certain number of years to qualify as an MBA, we can use the course as a marketing tool." A trip abroad - possibly to Tennessee - to see how overseas schools operate will be one of the attractions on offer.
The authority has earmarked funding to allow 24 people to attend the course in the first year, but it hopes to offer all heads and deputies an opportunity to get the qualification. The course is part of a pound;100,000 package aimed at improving leadership in Hull schools. The course will include a series of lectures by internationally-known academics.
Angus Ogilvie, secretary of the Hull branch of the National Association of Headteachers, welcomed the scheme. He said: "This isn't a lot of money for quality training and would be money well spent."