It happens to everyone who takes frequent showers and lets the plastic shower curtain or liner drape into the bathtub or shower stall: the curtain gets moldy. That black gunk is not only unsightly, it's bad for you, promoting the growth of fungus and creating a respiratory hazard in sensitive individuals. It also spreads, and it can discolor tile grout and painted walls. You don't need to let things go so far, though. Getting the mold off a plastic shower curtain or liner doesn't require specialty cleaners, and you don't have to spend time scrubbing the curtain, either.
Take down both the shower curtain and the liner. The easiest way to do this is often to take down the curtain rod, slide the curtain and liner off, and then remove the hangers. If your rod doesn't come down easily, remove the hangers one-by-one by bending them apart and slipping the curtain off.
Put the moldy curtain in the washing machine with two medium-size bath towels. Set the cycle selector to gentle and add a 1/2 cup of baking soda to the same amount of laundry detergent. Allow the machine to proceed through the wash cycle, then add 1/2 cup of white vinegar to the rinse cycle. Remove the curtain and let it drip dry.
Use bleach to remove stubborn mold. Put the curtain in the washing machine with two bath towels, set the water temperature to warm and the cycle to gentle, and let the machine run without adding anything.
Add 1/2 cup of chlorine bleach and 1/4 cup of detergent to the water after two or three minutes and let the washer run all the way to the end of rinse cycle.
Put the curtain and the towels in the dryer and run it on low heat for 10 minutes. Remove the shower curtain and hang it to drip dry the rest of the way.