Monika Maldrik says she finished all the assignments for a Higher National Diploma in health and social care management at ABI College, west London.
Ms Maldrik says the delay meant she "lost a year".
The college says it will contest the order made by the County Court Money Claims Centre in May.
The certificate for the course, which ran from September 2013 until May last year, was finally issued in mid-June this year and the college has told Ms Maldrik it is ready to collect.
Her statement to the County Court Money Claims Centre says she paid more than £5,800 in tuition fees for the full-time course.
"Unfortunately, I did not get the service for which I paid," she says in the statement.
The college rejects Ms Maldrik's criticisms of her course but accepts that changes in teaching personnel did cause some delays in marking assignments.
Ms Maldrik, who works for the minimum wage as a carer says she has so far been unable to apply for better jobs because of the delay in issuing the certificate.
The order, which was issued in May after the college did not respond to Ms Maldrik's claim, tells the institution to pay Ms Maldrik, who now lives in Margate, £5,000, including £205 costs.
The college is now applying to have the order set aside and says it will contest the claim.
The college told Ms Maldrik the late issuing of the certificate was due to a block being placed on some candidates by the exam board Pearson which runs the HND qualifications.
A spokesman for Pearson said the exam board was unable to comment on individual cases but said it employed a rigorous set of checks "to enable us to have confidence in any centre which delivers our qualifications which can, on some occasions, result in centres being blocked until any issues have been addressed.
"We regret any distress that this process may cause to students but we have a duty to ensure that standards are upheld nationally so that students, universities and employers can remain confident about the performance of students who complete our courses."
A private college has been ordered to pay £5,000 to a former student who claimed that a certificate for a course she completed was issued a year late.