The Dragonfly Nebula (G75.2+0.1) powered by the young pulsar J2021+3651 is a rare pulsar wind nebula (PWN) that shows double tori and polar jets enclosed by a bow-shock structure in X-rays. We present new radio observations of this source taken with the Very Large Array at 6 GHz. The radio PWN has an overall size about two times as large as the X-ray counterpart, consisting of a bright main-body region in the southwest, a narrow and fainter bridge region in the northeast, and a dark gap in between. The nebula shows a radio spectrum much softer than that of a typical PWN. This could be resulting from compression by the ram pressure as the system travels mildly supersonically in the interstellar medium. Our polarization maps reveal a highly ordered and complex B-field structure. This can be explained by a toroidal field distorted by the pulsar motion.