Device (11) for infusing a fluid substance into the body of a living being, comprising a hollow duct body (13) in which a rectilinear distal portion (15), a middle portion (17) and a proximal portion (19) are defined, wherein the distal portion (15) terminates with a pointed end (21) and extends along an axis substantially perpendicular to a plane in which the middle portion (17) extends, characterized in that the middle portion (17) comprises a curved section (23).