An electro-optical tunable filter comprised of two paralleled identical long-period waveguide gratings is proposed in this paper. The filter has one input port and two separate output ports, outputting band-pass and band-rejection light respectively. Using poled electro-optical polymer material to fabricate its waveguide cores enable the filter's tuning speed to approach nanosecond order. With the aid of long-period waveguide gratings, the tuning range of the filter is Λ times larger than the conventional electro-optical filters. We built up a model to design and simulate the proposed tunable optical filter. We investigate the relationship between the parameters of the long-period waveguide grating and the characteristics of the tunable filter, such as tuning range and FWHM. The simulation results show that the tunable optical filter can realize high-speed tuning in the wavelength range of 1530 nm to 1560 nm, and the FWHM width can reach 0.8 nm. Compared with the conventional optical filters, the results show that a high-speed widely tunable optical filter with narrow pass band can be achieved.