Jay-Z -- aka Shawn Carter -- is being sued by Air Platinum Holding, a private jet company which claims Jigga spent 55 hours on their planes back in 2009 ... but only paid for 37 hours of service.

The suit also claims Jay-Z flaked out on some other payments as well -- here's how it all breaks down:

-- 18 hours of flight time at $4,500-per-hour (discounted from $6,000-per-hour) ... $81,000
-- Catering for 17 domestic flights ($500-per-flight) .... $8,500
-- Catering for 4 international flights ($750-per-flight) ... $3,000
-- International fees ... $8,500
-- Taxes ... $12,285
-- Luxury trip to England ... $24,200

It all adds up to $137,485.00 ... which is why most people just fly coach.