  The first author and Oguni introduced a wide class of metric spaces, called
coarsely convex spaces. It includes Gromov hyperbolic metric spaces, CAT(0)
spaces, systolic complexes, proper injective metric spaces. We introduce the
notion of free products of metric spaces and show that free products of
symmetric geodesic coarsely convex spaces are also symmetric geodesic coarsely
convex spaces. As an application, it follows that free products of symmetric
geodesic coarsely convex spaces satisfy the coarse Baum-Connes conjecture.
