A so-called double-pyramid waveguide network composed of one-dimensional optical waveguide segments is constructed and the properties of photonic band gap (PBG) and photonic attenuation by means of network equation, generalized Floquet-Bloch theorem, and generalized eigenfunction method are investigated. It is found that huge absolute PBGs and extreme strong photonic attenuation can be generated by this interesting optical waveguide network, which includes high density of triangular fundamental loops. When each pair of nearest-neighbor nodes in the network are connected by two waveguide segments with the length ratio of 2∶1, the ratio of the absolute PBG Δω to the midgap frequency ΔωC arrives at 154% . The average photonic attenuation of the largest PBG resulted from this two-segment-connected network with 8 unit cells is stronger than 10-21 (which is equivalent to -210 dB). This interesting optical waveguide network may be useful for the designing of optical devices with large PBG and strong attenuation.