NHS Tayside had the highest number followed by NHS Lanarkshire  and NHS Greater Glasgow and Clyde.
The figures also revealed that more than 560,000 people missed at least one NHS outpatient appointment in 2014/15.
Each missed appointment is thought to cost the NHS Â£120, putting the total cost to the health service at Â£100m.
The figures were obtained by the Scottish Conservatives through a Freedom of Information request.
The statistics revealed:
The Scottish Tories have previously suggested those who fail to show for appointments on a certain number of occasions could face some sanction from the health board.
The party has also urged the Scottish government look at more innovative ways of reminding patients to turn up at appointments.
Scottish Conservative leader Ruth Davidson said: "Missing a hospital appointment can happen to anyone, and for a range of reasons.
"But when you're getting to the point where you are missing five or more in the space of just a year, something really has to be done.
"That is costing the NHS thousands of pounds, wreaking havoc with hospital planning, and of course potentially harming the health of the patient involved.
"We've been critical of the NHS in the past for cancelling appointments and procedures, so it's only fair we do everything we can to make sure patient no-shows are limited too.
"We need to find ways to ensure people turn up at the appointments that are made and stop showing contempt for our NHS, doctors and nursing staff."
Health Secretary Shona Robison said the percentage of patients missing appointments has decreased slightly over the last five years.
She added: "However, it is important that all health boards understand why patients are not attending appointments and look at ways to reduce this.
"The Scottish government is committed to supporting health boards to deliver secure messaging services, including reminders.
"Health Scotland also recently published a report looking at those who did not attend appointments over a 10 year period from 2002/03 to 2011/12.
"We welcome this report which will provide boards with further learning on the issue of non-attendance."
Nearly 17,000 patients in Scotland failed to show up for an NHS hospital appointment on at least five occasions last year.