Recently, some kinds of structures have been found to show the property of extraordinary optical transmission (EOT). In this paper, we present a novel composite structure based on array of annular apertures (AAA) with compound lattice. The lattice includes two kinds of annular apertures with the same outer radius and different inner radii. The transmission spectrum of this compound periodic AAA can be achieved by adding up the spectra of two corresponding simple periodic AAAs, and the transmission shows EOT property. The transmission peaks of this kind of structure can be adjusted to desire wavelengths by changing the inner radius of aperture or the index of the dielectric material in the aperture. This structure can be used as a filter with dual pass bands when the difference between inner radii or indices of dielectric inside is large enough for two kinds of apertures.