The 45-year-old from Perth, Australia, has collected lint every day for 26 years.
He 'harvests' the lint each night and places it in a clay pot, while he waits for his shower to warm up.
He has now filled three and a quarter sweet jars and had his achievement recognised by Guinness World Records.
Graham, who says he is 'not obsessive', collected his first piece of fluff on 17 January 1984 while on a backpacking holiday in Australia.
He vows to continue until he is no longer capable - and has even considered stuffing a cushion with his collection.
He said: 'One evening in Brisbane, when a little bored and under-occupied, I noticed the lint in my navel and started wondering about it.
'I became curious as to how much of it one person can produce and decided the only way to find out was to collect it for a while and see.
'I had an empty film canister with me, which became a perfect receptacle.
'That's all there was to it - no obsession or grand plan, just simple curiosity.'
Mr Barker said the amount of fluff he collects each day depends on what clothes he has been wearing - with thermal underwear being the most 'productive'.
He added: 'I found that having a shower tends to wash away any lint, so the logical time to collect is just before getting in the shower each evening.
'I turn on the taps then pluck and store while waiting for the water to heat up.
'The whole process only takes about ten seconds and has become automatic - I don't need to devote much time or attention to it.'
At the end of each year the small collection is added to his main collection, which is housed in larger jars.
The colour of the fluff varies, depending on what colour towel Graham uses.
It never goes mouldy and does not smell, which means lint from 20 years ago is 'indistinguishable' from the new stuff.
Mr Barker has now sold three of his large jars to a museum for an undisclosed sum and is a quarter of the way to filling the fourth.
He said: 'The raw material is worthless but as a unique world record collection and a piece of cultural heritage, of debatable merit, it has some curiosity value.
'The overwhelming majority of people have a positive reaction. They are amused or surprised that such a collection exists.
'A few, usually women, recoil in mock horror, thinking that lint from a navel is really gross.
'And some think I must have too much time on my hands, which always strikes me as an illogical thing to say about a habit which only occupies ten seconds per day.
'A small minority with no sense of humour just don't get it and express their opinion with rude words.'
Mr Barker knows a few other navel fluff collectors but says he rarely talks to people about his bizarre antics.
He said: 'Collecting is not a big part of my life so I generally don't talk about it or ask others about it.
'When I ran my navel lint survey many years ago a handful of respondents, who were all men, confessed to having saved up some of their lint at some point.
'But none had continued with it.
'One guy might have persisted, but he got married and his wife ordered him to stop.'
Mr Barker hopes to fill another five jars before he stops collecting and believes there is little chance of his record being beaten.
He said: 'I will stop collecting when I'm no longer physically capable.
'Collecting lint costs nothing and takes almost no time or effort so there is no compelling reason to stop.
'In fact most days my lint collecting gets as much conscious thought as other routine tasks like putting on socks.
'I wouldn't call it an addiction because it's not something I feel any need to do.
'If my belly stopped producing lint tomorrow I might feel surprised but not disappointed.'