A novel woodpile lattice structure is proposed. Based on plane wave expansion (PWE) method, the complete photonic band gaps (PBGs) of the novel woodpile three-dimensional (3D) terahertz (THz) photonic crystal (PC) with a decreasing symmetry relative to a face-centred-tetragonal (fct) symmetry are optimized by varying some structural parameters and the highest band gap ratio can reach 27.61%. Compared to the traditional woodpile lattice, the novel woodpile lattice has a wider range of the Riling ratios to gain high quality PBGs, which provides greater convenience for the manufacturing process. The novel woodpile 3D PC will be very promising for materials of THz functional components.