A novel composite electrolyte SDC-(Li/Na)₂SO₄ was prepared for intermediate temperature solid oxide fuel cells (ITSOFC). The phase structure and cross-sectional morphology were examined by XRD and SEM, respectively, and the ionic conductivity was investigated by AC impedance in a temperature range of 400 ^oC ~ 700 ^oC in air. It was found that the composite electrolyte was composed of two phases: crystal SDC and amorphous (Li/Na)₂SO₄. The conductivity of the composite electrolyte was significantly larger than that of SDC at intermediate temperatures (550 ^oC ~ 700 ^oC) and increased with temperature in three stages: 1) T<500 ^oC, the apparent activation energy of ionic transport was 1.28 eV; 2) In the range of 500 ^oC ～ 550 ^oC, the ionic conductivity rapidly increased due to the melting of sulfate; 3) T>550 ^oC, the conductivity slowly raised with temperature, the activation energy decreased significantly to 0.30 eV, and the values of the conductivity of SDC-(Li/Na)₂SO₄ were notabily higher than those of SDC and previously reported SDC-(Li/Na)₂CO₃. For example, the conductivity of SDC-(Li/Na)₂SO₄ was 0.217 S·cm^-1 at 550 ^oC, which was 25 times higher than that of SDC and 3.2 times higher than that of SDC-(Li/Na)₂CO₃. The results indicate that the ionic conducting mechanism changes in composite electrolyte due to the melting of the sulfate second phase, and the diffusion and transmission of ions are accelerated.