An intracavity, second-harmonic generation, tunable, dual-frequency, passively Q-switched Nd:YAG laser based on a T-resonator configuration with polarization splitting is proposed, whose frequency difference could be doubled in comparison with fundamental lasing. The Nd:YAG, Cr^{4 +} : YAG, and potassium titanyl phosphate (KTP) crystals were set at the shared arm, which could considerably reduce thermal fluctuation and pulse timing jitter between dual-frequency lasers. One birefringent filter consisting of a polarized beam splitter and a half-wave plate (HWP) is placed in each divided arm to select their single longitudinal mode. As a result, the p-polarized and s-polarized passively Q-switched components of 532 nm are simultaneously operated, whose power easily reaches to same and frequency is beneficial to tune theoretically throughout the whole gain bandwidth. The main characteristics of the power, longitudinal mode selection, and the pulse have been tested experimentally. Moreover, the frequency difference of the dual-frequency laser at 532 nm has been widely tuned from 9.6 to 117 GHz, by slightly adjusting the tilt angles of the HWPs. We offer a simple and widely tunable source with potential for portable frequency reference applications in absolute-distance interferometry, terahertz-wave generation, and other fields.