Yes, it is safe to eat fish when you're breastfeeeding, as long as you stay away from fish with high levels of mercury, which can damage a baby's nervous system.
The Environmental Protection Agency and U.S. Department of Agriculture advise breastfeeding women to completely avoid four specific types of fish: shark, swordfish, king mackerel, and tilefish. Solid white or albacore tuna also tends to be higher in mercury than other types of canned tuna, so you should limit your intake to no more than 6 ounces per week.
That said, it's great for a breastfeeding mom to eat certain other kinds of fish, because fish's omega-3 fatty acids give your baby's developing brain a real boost.
A study by Harvard Medical School and Statens Serum Institute in Denmark found that higher fish consumption in breastfeeding moms is linked to better physical and cognitive development in infants.
Children whose mother ate an average of 2 ounces of fish per day had babies who were 25 percent more likely to have higher developmental scores at 6 months old.