A twisted-mode cavity end-pumped dual-frequency Nd∶YAG laser has been presented. The polarizing beam splitter is used as the polarizer and two quarter-wave plates are placed on each end of the gain medium Nd∶YAG crystal. The frequency difference of the dual-frequency laser can be continuously tuned through the whole cavity free spectral range, by rotating one of two quarter-wave plates in the plane perpendicular to the cavity axis. The theoretical analysis based on Jones matrices is made that the frequency difference is proportional to the rotation angle of the wave plate. The characteristics of twisted-mode cavity mode selection, mode splitting and polarization have been investigated experimentally. The results show that laser is output with the linearly polarized single longitudinal mode when the two quarter-wave plates are perpendicular, and the single longitudinal mode splits into two modes which are orthogonally linearly polarized modes while the twisted-mode cavity is detuning. The largest frequency difference obtained is about 3 GHz. Experimental results match well with the theoretical analysis. Such a continuous tunable dual-frequency Nd∶YAG laser with simple structure will find wide applications in the fields of laser interferometry, and microwave photoelectronics, etc.