Use newspaper. Put your old paperback books in a container that can be tightly closed. Crumple up sheets of newspaper and put in the container with the book(s). Every day change the newspaper replacing with new crumpled sheets for a few days. Within 3 or 4 days your book should not have that musty smell and the odor will be absorbed by the newspaper.
Ground Coffee. This method takes a little longer (about 2 weeks) to work. Place a tablespoon or two of regular ground coffee in a zip lock bag and then put the book in the zip lock bag. The coffee will rid the book of that nasty musty smell.
Use dryer sheets. Those fabric dryer sheets we use in the laundry will help rid a paperback book of that musty smell. Use a scented dryer sheet and place it in the book and then place the book in a tightly closed container and the odor will disappear from the book in a few days.
Baking Soda and a coffee filter. Pour some baking soda into a coffee filter and either tie, rubber band or twist tie the top of the coffee filter closed. Then take your book and the filter baggie of baking soda and place in a zip lock bag. Place in the freezer for a few weeks and the smell will be gone.