Select a cleaner that removes or kills moss on fiberglass asphalt shingles. If it states it removes algae, it will also work on moss. Cleaners made with an oxygen bleach may be more environmentally friendly than other products. For easy use, select one with an applicator built in. Otherwise, you will need a pump sprayer. You will also have to dilute the cleaner according to the manufacturer's directions.
Spray the product on the roof as directed on the label. This is best applied in the spring or fall, according to Popular Mechanics. After the moss dies, which can take a week or more, proceed to the next step. You may need to reapply the product, however, if some of the moss is still alive.
Spray a pressure washer to remove the dead moss. Start at the top of the roof, pointing it down toward the ground so you don't spray water up and under the fiberglass shingles, causing a leak. Begin with a low setting, holding it at least 12 to 24 inches away. Increase pressure and hold the wand closer as necessary, being cautious not to damage the fiberglass panels. The power washer will loosen and wash away the moss from the roof.