Measure the length and width of your futon mattress. Take into account the depth of the mattress when taking your measurements as the fabric will need to cover the sides. Add an extra 2 inches all the way around for hemming. Cut out two identical pieces of fabric to the necessary measurements for the front and back of the futon cover.
Lay the two pieces of fabric on your work surface, one piece on top of the other with the right sides together. Pin the edges together along the two long sides and one of the short sides.
Sew around the pinned sides 2 inches from the edges. Trim away any excess fabric, especially at the corners.
Turn the futon cover right side out. Poke out the corners to make them sharp.
Fold under the fabric edges on the remaining open side. Make a 1/4-inch fold along the edge and then make another 1/4-inch fold to enclose the raw edges. Use pins to hold the fabric in place. Sew along the folded edges to secure the hem in place and then trim any threads.
Slide the futon mattress into the futon cover. Hand sew the open ends together if you want your cover permanently closed. If you prefer to be able to remove the futon mattress and wash the cover, close the opening using safety pins.