The 62-year-old singer was diagnosed with colon and liver cancer last year, but has since revealed he's in remission following chemotherapy and radiotherapy.
Robin's twin Maurice died in 2003 aged 53, while brother Andy passed away aged just 30 in 1988.
"I sometimes wonder if all the tragedies my family has suffered, like Andy and Maurice dying so young and everything that's happened to me recently, is a kind of karmic price we are paying for all the fame and fortune we've had," Robin told The Sun.
"But we've worked hard for everything we've achieved. The illness, and the untimely death of my brothers, has made me conscious of the fact that - rather than just think about it - it's crucial that you do today what you want to do.
"I've got a sense of urgency about life, rather than withdrawing from it and feeling depressed. Now I know how precious time is, and that you can't put it in the bank. So I intend to make the most of every single second of it that I've got left."
Robin was originally taken to hospital in 2010 after becoming unwell while performing on stage in Belgium.
"I was told that I had to have an emergency operation on my colon right away because I had a blockage in my intestine. I went into shock there and then, because my twin Maurice had died of exactly the same thing in 2003," he said.
Robin will sing his new song 'Don't Cry Alone' at London's Concert Hall on April 10 as part of the world premiere of his classical score The Titanic Requiem. The project was written alongside son RJ and is performed by the Royal Philharmonic Orchestra.
Listen to Robin Gibb's 'Don't Cry Alone' below: