John McCormack was speaking as the society launched its annual daffodil day collection, which is taking place on 7 March this year.
The society says an ageing population is one of the main reasons for the predicted increase in cancer cases between now and 2020.
In 2005, more than 25,000 cancer cases were diagnosed. Figures from the National Cancer Registry indicate that by 2020 that figure may increase to almost 42,000.
Today, the Irish Cancer Society said the increase is primarily due to an ageing and growing population but a general neglect of healthy lifestyle is also playing a role.
Mr McCormack said Ireland's growing cancer problem could be helped by the Government's Cancer Control Programme.
Speaking about the report into cancer misdiagnosis at the Midland Regional Hospital in Portlaoise, he urged the Government to publish the report of Dr Ann O'Doherty as soon as possible.
He said serious lessons need to be learned from what happened in the Midlands.
The report, which had been due to be published last December, has still not gone to Government.
