This study investigates the propagating of electromagnetic waves through a one-dimensional quasi-photonic crystal with the transfer matrix method. Our proposed structure consists of two types of double negative metamaterials, organized according to the Thue-Morse sequence law. The results show that changing the structure via quasi-periodic arrangements makes the outcome more varied than applying the absolute periodic arrangement. Given that, our desirable results of interest are more conveniently achieved. The structure completely stops-both s and p polarization at the lower frequencies, for all incidence angles. It also partially stops s and p polarization, at higher frequencies. Moreover, the achieved transmittance spectrum contains several omnidirectional band-gaps, which remain invariant with changes in the incidence angle. The oscillation of the transmittance values also becomes more intense at higher orders of the period number. This study could pave the way for optimizing of photonic crystal circuits, splitters, switches, etc.