The damp musty smell on a mattress is a result of mold and mildew. Mildew will form on the mattress in damp and humid conditions, and can range in color from white, black and green. The mattress needs to be cleaned properly and safely to remove the smell as well as the mildew. Cleaning the mattress promptly can prevent the mildew from growing and ruining the material.
Vacuum the entire mattress to help remove mold and mildew areas. Empty the vacuum cleaner once you finish or throw the bag out immediately so that you do not spread the mildew.
Combine an equal amount of water and rubbing alcohol. Dampen a washcloth with the solution and clean the surface of the mattress to kill the mildew. Rinse the areas with warm water to remove the solution.
Mix an equal amount of white vinegar and water in a spray bottle. Spray the solution over the mattress and then sprinkle baking soda over the surface. Allow the mattress to dry overnight, and then vacuum the baking soda off the mattress to remove the smell.
Place the mattress outdoors in the sun to dry quicker. The sun will also help destroy the mildew. If you cannot place the mattress outdoors, stand it against a sunny window, open the window and turn on a fan to speed up the drying process.