Abstract: Recently Left Handed Photonic Band Gap (LHPBG) structures have become the object of intense experimental and theoretical researches due to their novel properties. Most of the early research efforts were concentrated on the analysis of the LHPBG structures consisting of materials with special frequency dependent parameters, such as Drude model for ε and μ of the structure. In this study, first the complete Drude-Lorentz model is introduced for the constitutive parameters of materials and a real one-dimensional structure is analyzed. Then a complete one dimensional left handed photonic band gap with multiple defect states is investigated. For computation of the band structure and transmission spectra of real frequency dependent structures with and without defects, the dispersive finite-difference time-domain method has been used. The effects of number of layers, defects and variation of parameters of spatial dispersion of layers to the band gap of the structure are studied. A multiple channel filtering by variation of the band gap structure is proposed.