Place the tablecloth on top of a level surface covered with a towel. Keep the mildew facing upward toward the ceiling.
Moisten a cloth with white vinegar and blot the mildew for several seconds until saturated. White vinegar will help kill the fungus.
Turn the washing machine to the hottest water temperature allowed for the linen tablecloths. Add 1/4 cup of laundry detergent and 1 cup of bleach to the water. Use chlorine bleach for white tablecloths and a color-safe or oxygen bleach for colored linens.
Place the linens in the washing machine and submerge them in the water. Close the washer lid and let the washing machine complete a full wash, rinse and spin cycle.
Remove the tablecloth from the washing machine. Soak it in a bucket filled with equal parts water and oxygen bleach for 30 minutes if mildew stains remain.
Launder the tablecloth in the same manner as before. Tumble dry on low heat.