In order to further investigate the non-reciprocity of light propagation in the defective atomic lattices, and due to its effective application in designing novel photonic devices, such as all-optical diodes and isolators, which are powerful tools for information processing and quantum simulation, we innovatively propose to use the Fibonacci sequence to modulate the arrangement of empty lattice cells that form a quasi periodic defective atomic lattices. In the electromagnetically induced transparency window, the probe light is almost not absorbed under the control of a strong coupling field (see Fig. 1). The numerical simulation indicates that a wide nonreciprocal reflection band can be achieved by modulating the number of filled lattice cells, Fibonacci sequence, the period number in a single quasi period (see Fig. 2). These results provide more degrees of freedom for regulating nonreciprocal reflection with wide bandwidth and high contrast, and have potential applications in quantum computing and information processing.