A novel dual-polarization fiber laser is proposed by incorporating a distributed feedback grating inscribed in a twin-hole fiber with internal electrodes. Dual-polarization lasing is achieved with a spectral separation of ~42 pm. By beating the optical waves at a photodiode, a microwave signal at ~5.244 GHz is achieved with a signal-to-noise ratio ~45 dB. An electrically tuned microwave signal with a tunable range of 150 MHz is demonstrated.