In order to produce the dual-frequency laser with tunable frequency-difference at 1 064 nm, a two-cavity dual-frequency Nd∶YAG laser was designed using a twisted-mode configuration, the two standing-wave cavities of which share the same gain medium Nd∶YAG, and the twisted-mode configuration reduced or even eliminated the spatial hole-burning effect of gain so that the single longitudinal mode can be oscillated in both standing-wave cavities of the Nd∶YAG laser, thus the orthogonally and linearly polarized dual-frequency laser at 1 064 nm was obtained. The principles of both single longitudinal mode selection of the twisted-mode configuration and the simultaneous oscillation of the dual-frequency laser were theoretically analyzed, and the characteristics of dual-frequency laser oscillation and frequency difference tuning were investigated experimentally. The experimental results show that both cavities of the Nd∶YAG laser can steadily oscillate in linearly polarized single longitudinal mode, and the frequency-difference can be tuned up to one longitudinal mode interval by changing the cavity length, the frequency-difference tuning range is 0.3 GHz to 3 GHz.