In this work, the theoretical and experimental study on vibration transmission in quasi-periodic impedance layered structures built by magnetorheological (MR) fluid is conducted. Based on the MR effect of MR fluid, the quasi-periodic layered structures formed by low and high impedance layers following Fibonacci, Thue-Morse and multiperiodic sequences are constructed, respectively. These different quasi-periodic patterns can be flexibly obtained by controlling the arrangement style and magnetic field strength of electromagnets outside the MR fluid. The vibration transfer model is established based on the transfer matrix method and the trends of vibration level difference with different parameters are analyzed. Furthermore, experiments are performed to estimate the vibration transmissivity of the proposed structures. It indicates that the developed quasi-periodic impedance layered structures can exhibit greater damping effect on vibrations by appropriately increasing the magnetic field strength and thickness ratio of low to high impedance layers. Moreover, there exist quasi-periodic impedance patterns whose attenuation effect on vibration is better than that of periodic pattern in the frequency range studied in this paper (20~200Hz). This means that the introducing of the particular quasi-periodicity increases the transmission loss of vibrations in a certain frequency range. This investigation is conducive to further expand the application of MR materials and quasi-periodic structures in the field of vibration control.