A structure of symmetric generalized Fibonacci photonic crystal is proposed to design the electrooptical tunable filters based on the electrooptical effect of LiNbO3 material. The characteristics of the tunable filter are theoretically investigated by the transfer matrix method. The numerical simulation results show that the channel wavelength of the filter can be modulated by the external electric field which is applied on the LiNbO3 layers without changing the geometrical structure of the symmetric generalized Fibonacci photonic crystal, and the channel wavelength will linearly move to short wavelength as the increase of the external electric voltages. In addition, if the external electric voltage is fixed, the channel wavelength will move to short wavelength as the increase of the incident angle; if the incident angle is fixed, the channel wavelength will move to short wavelength for the increase of plus external electric voltage, while the channel wavelength will move to long wavelength for negative external electric voltage. Lastly, the characteristics of the tunable multichannel filter with double external electric fields are discussed. It provides an important reference for design of novel photonic crystal devices.