Because shrimp is highly perishable, the vast majority offered to consumers in markets and grocery stores are frozen or were previously frozen. It doesn't mean that you shrimp isn't fresh, however. Good quality shrimp will be flash-frozen immediately after being caught to maintain their flavor and texture. Frozen shrimp can and does go bad, especially if you purchased some that may have been previously frozen, thawed by the fish counter and then frozen again when you brought it home.
Place the frozen shrimp in the refrigerator to thaw completely. Thawing the shrimp is the only way for you to be able to accurately smell, touch and look at them for signs of spoilage.
Smell the shrimp. The shrimp should have a very mild ocean or salt-water smell. If it has any type of strong, unpleasant odor, including a chlorine, iodine or ammonia odor, throw it out, as these are clear indications of spoiling or improper preparation or handling.
Look at the shrimp. Your thawed shrimp should be translucent and shiny. If you have shell-on shrimp, the shells should be smooth, firm and clinging tightly to the shrimp. Toss out shrimp if most of the shells are hanging off. If the heads are cut off, as most frozen shrimp are, the exposed meat should be pure white. If it is pink, the meat is deteriorating and should be discarded.
Touch the shrimp. They should feel wet but not slimy. Sliminess can indicate bacteria growing or an excessive use of chemicals when processing the shrimp.