Yes, you can surf on a paddle board. When buying a paddle board for surfing, you need to remember to get one that can handle the activity. People often get paddle boards and think they will work for everything, only for them to realize they cannot use them for surfing. Talk to the staff at the shop and figure out how you can use your paddle board. That way, you are sure you have a paddle board suitable for other activities and will help prevent damage to the board itself.