The researchers are calling for more help and support to be targeted at people with lower IQs.
Their findings were published in the journal Psychological Medicine.
The researchers, at University College London, analysed data from the Adult Psychiatric Morbity Survey in England.
One of the questions was: "Taking all things together, how would you say you were these days - very happy, fairly happy or not too happy?" People's verbal IQ was also assessed.
The highest proportion saying they were "very happy" was found in people with an IQ between 120 and 129 - 43% said they were very happy.
However, the highest proportion saying "not too happy" - 12% - was found in people with an IQ between 70 and 79.
Dr Angela Hassiotis said: "People in the lower end of the normal spectrum are more likely to consider themselves not happy."
The study said lower intelligence was linked to lower income, worse health and needing help with daily life, such as shopping or housework - all of which contributed to unhappiness.