The transmission properties of Thue-Morse quasi-periodic one-dimensional photonic crystals (1DPCs) containing superconducting material are theoretically investigated based on the transfer matrix method. It is shown that the 1DPCs can possess a same photonic band gap property as the periodic structure superconducting PC. The results of transmittance spectra show that the cutoff frequency can be manipulated through the thicknesses of the superconductor and dielectric layers as well as the ambient temperature of the system. It is observed that the shift of cutoff frequency becomes more noticeable by adjusting the thickness of the superconductor layer than that of the dielectric one. Furthermore, the cutoff frequency becomes very sensitive when the system temperature is tuned to close vicinity of the critical temperature of the superconductor.