The British Lung Foundation carried out a survey of 1,000 adults and found a third wrongly believed cannabis did not harm health.
And 88% incorrectly thought tobacco cigarettes were more harmful than cannabis ones - when the risk of lung cancer is actually 20 times higher.
The BLF said the lack of awareness was "alarming".
Latest figures show that 30% of 16-59 year-olds in England and Wales have used cannabis in their lifetimes.
A new report from the BLF says there are established scientific links between smoking cannabis and tuberculosis, acute bronchitis and lung cancer.
Cannabis has also been shown to increase chances of developing mental health problems such as schizophrenia.
Part of the reason for this, say the experts, is that people smoking cannabis take deeper puffs and hold them for longer than when smoking tobacco cigarettes.
This means that someone smoking a cannabis cigarette inhales four times as much tar as from a tobacco cigarette, and five times as much carbon monoxide, the BLF says.
Its survey found that young people are particularly unaware of the risks.
Almost 40% of the under-35s surveyed - the age group most likely to have smoked it - thought cannabis was not harmful.
However, each cannabis cigarette they smoke increases their chances of developing lung cancer by as much as an entire packet of 20 tobacco cigarettes, the BLF warned.
Its chief executive, Dame Helena Shovelton, said: "It is alarming that, while new research continues to reveal the multiple health consequences of smoking cannabis, there is still a dangerous lack of public awareness of quite how harmful this drug can be.
"This is not a niche problem - cannabis is one of the most widely-used recreational drugs in the UK, with almost a third of the population having tried it.
"We therefore need a serious public health campaign - of the kind that has helped raise awareness of the dangers of eating fatty foods or smoking tobacco - to finally dispel the myth that smoking cannabis is somehow a safe pastime."
The BLF's report says there should be a public education programme to raise awareness of the impact of smoking cannabis and increased investment in research into the health consequences of its use.