In order to produce the single frequency tunable laser output at 1064 nm, a diode-pumped electro-optically tunable single frequency Nd:YAG laser is designed, which includes an electro-optically birefringent filter (PBS-LN) consisting of both a polarizing beam splitter (PBS) and a lithium niobate (LN) crystal, used as both a single longitudinal mode selector and a frequency tuning element. The principles of mode selection and frequency tuning of the PBS-LN are theoretically analyzed, and the characteristics of single longitudinal mode oscillation and frequency tuning of the Nd:YAG laser at 1064 nm are investigated experimentally. The experimental results have shown that the Nd:YAG laser can steadily oscillate in linearly polarized single longitudinal mode, and by changing the transverse voltages applied to the LN element, the wavelength of single longitudinal mode laser at 1064 nm can be tuned by 0.474 nm, corresponding to the frequency tuning of 142.2 GHz. Such an electro-optically tunable single frequency Nd:YAG laser will find wide applications in the fields of laser interferometry, laser radar detection and laser spectroscopy, etc.