Yes, of course, you can! To effectively paint over concrete, you must take these simple steps:
The concrete must be cleaned from dirt, grease, and/or oil.
The old paint has to strip. If it is interior concrete it's a good idea to also seal the concrete. Interior sealing is essential to preventing moisture from seeping in and preventing mold development.
The concrete must be primed.
Masonry paint is a great choice, especially for outdoor concrete, since they block off moisture penetration.