An NHS Blood and Transplant survey of more than 1,500 people showed that more than half those over 55 think they are too old, or too ill, to donate their organs.
But the organisation said donors from all age groups and ethnic backgrounds were required.
More than 10,000 people are currently in need of a transplant in the UK. Of these, 1,000 will die before getting an organ, which equals three people every day.
Associate medical director at NHS Blood and Transplant Professor James Neuberger said: "The belief that there is some sort of age limit on becoming an organ donor is a complete myth.
"There are also very few illnesses that prevent someone from donating their organs after death - that's why we would encourage anyone who wants to sign up to the NHS Organ Donor Register to do so and ensure those close to them are aware of their wishes."
There are only 13 donors per million people of population in the UK, giving it one of the lowest rates of organ donation in Western Europe. The highest rate in the region is in Spain, with 35 donors per million of population.