We demonstrate a parabolic reflector nanoantenna as a structure for directivity-enhanced Raman scattering (DERS). This antenna consists of a nanoscale paraboloid shaped Au reflector and an Ag nanoprism feed element. We experimentally test this nanoantenna and obtain a 22× enhancement to the Raman signal from nanoantenna structures with planar reflectors, and estimate a 1100× enhancement to the surface-enhanced Raman scattering (SERS) from the Ag nanoprism alone. A comprehensive finite-difference time-domain simulation is used to model the field intensity in the parabolic reflector nanoantenna, confirming its better coupling between the near- and the far-field. Moreover, we describe a possible method to obtain an even higher SERS gain from our structure.