A cost-effective technique for coupling a polymer optical fiber (POF) with 50 μm core diameter to a silica single-mode fiber (SMF) with 8 μm core diameter is proposed, which can, by exploiting a multimode fiber with 50 μm core diameter, avoid the damage or burning at the butt-coupled POF/SMF interface. Using this coupling technique, we also show that the Brillouin signal in a POF can be enhanced by combined use of pulsed pump and an erbium-doped fiber amplifier. When the pulsed pump with average optical power of 18 dBm (63 mW), duty ratio of 15%, and pulse period of 2 μs is launched into a 200 m-long POF, 4 dB enhancement of the Stokes power is obtained compared to that with 18 dBm continuous wave pump. The relatively small enhancement is probably caused by the high Brillouin threshold of POFs. The Stokes power dependence on duty ratio is nonmonotonic, which might originate from a longer phonon lifetime in POFs than that in silica SMFs.