High-temperature superconductor compound Tl2Ba2Can−1CunO2n+4+δ (n = 2, 3, 4) was prepared by solid-state reactionevacuated sealed tube method. The research was carried out to investigate the effect of parameter (n) on the superconductor behavior of the compound Tl2Ba2Can−1CunO2n+4+δ. The structural phase of prepared samples was analyzed by X-ray diffraction (XRD) analysis, and the results showed the demand phase depend on the parameter (n). The resistivity measurement by four-probe technique used to investigate the critical temperature. The parameter (n) has major effect on definition of critical temperature for superconductor compound. The results showed that the sample prepared with n = 2 has a critical temperature Tc= 102 K; meanwhile, the sample prepared with n = 4 has a critical temperature Tc= 99 K; however, the sample which was prepared with n = 3 has a maximum critical temperature Tc= 121 K. There is a match between the result of magnetic susceptibility and the resistivity measurements at n = 3.