The pump polarization direction can greatly influence the characteristics of the laser diode end-pumped monolithic microchip Nd:YAG dual-frequency laser. We experimentally observe the lasing thresholds and the optical powers of two splitting modes versus the pump polarization direction. The effect of the pump-induced gain anisotropy on the mode oscillation sequence is analyzed. And the effect on the intensities of these modes is also proved with a rate equation model. This study contributes to the improvement of the stability and the reliability of the Nd:YAG dual-frequency laser.