Omega-3 is a type of fat. Small amounts are essential for good health and can be found in the food that we eat including nuts and seeds and fatty fish, such as salmon.
They are also readily available as over-the-counter supplements and are widely bought and used.
The study, published in the British Journal of Psychiatry, found that omega-3 supplements offer no benefit.
"This large systematic review included information from many thousands of people over long periods," said study lead author Lee Hooper, from University of East Anglia in UK.
"Despite all this information, we don't see protective effects, the most trustworthy studies consistently showed little or no effect of long-chain omega-3 fats on depression or anxiety, and they should not be encouraged as a treatment," Hooper added.
For the findings, the research team looked at 31 trials of adults with and without depression or anxiety.
More than 41,470 participants were randomised to consume more long-chain omega-3 fats (fish oils), or maintain their usual intake, for at least six months
They found that the supplements had little or no effect in preventing depression or anxiety symptoms.
"Oily fish can be a very nutritious food as part of a balanced diet but we found that there is no demonstrable value in people taking omega-3 oil supplements for the prevention or treatment of depression and anxiety," said study researcher Katherine Deane.
( With inputs from IANS )