Asparagus should be stored in the refrigerator, not the freezer. Spread the spears out in a single layer on a tray or other pan that can go into the fridge.
Keep the tips wrapped in a damp paper towel, and store them in a plastic bag. Another method is to put the asparagus on a flat dish that can fit into your fridge, or even directly into a shallow glass or cup filled with water.
Asparagus has an optimum storage time of about two days. If you see any signs of spoiling, such as soft spears or a sour smell, use them immediately.
Do not store your asparagus in the plastic container that it comes in from the grocery store.
This will trap moisture and cause the bottom spears to turn slimy while protecting the ones on top from going bad.
The best storage method is to place the asparagus in a jar, shallow dish or tray. Make sure the spears are all laying flat and not touching each other.
The bottom of the container should be covered with either a damp paper towel or enough water to cover 1/4 of the spears.
So this is how to store Asparagus.