Clean your furniture. Use soapy water to remove any evidence of mold or mildew and dry the furniture with a towel. For a stronger clean, use one part water and one part bleach to wipe down your furniture. Allow your furniture to dry thoroughly before you begin to use it normally again. Sometimes a damp environment or musty room can promote a musty scent.
Run a dehumidifier in your bedroom to reduce the amount of moisture in the air. Even if you don't notice excess humidity, your furniture will. You can purchase a small, bedroom-sized dehumidifier at any home and garden store or at an allergy specialist store.
Place a small cup of coffee grounds inside the furniture. Allow the grounds to sit for a few days. Coffee grounds absorb odors and will minimize the musty scent of your wooden furniture.
Refinish the wood. Sometimes a musty odor just won't go away but a new finish will cover and reduce the scent. Hire a professional to refinish the wood or refinish it yourself for a more personal, hands-on experience. Allow the finish to dry thoroughly before you attempt to use the furniture. For the best results, place the furniture in a sunny area for a few days while it dries.