Solid state reaction method was used to prepare high temperature superconductor with a nominal composition Tl 2−x Hg x Sr 2 Ca 2 Cu 3 O 10+δ (0 ≤ x ≤ 1). The effect of quenching on the superconducting properties has been investigated by preparing two sets of samples at 1133 K for 3 hrs. The superconducting properties of the samples have been examined by electrical measurements. It is found that a partial substitution for Tl by Hg increases the formation of high-T c phase and increases its T c. X-ray diffraction (XRD) pattern analyses have shown a tetragonal structure, and there are at least two superconducting phases.