A new cobalt diphosphate (Na_0.71Ag_0.29)₂CoP₂O₇, is synthesized by solid state reaction method and characterized by single-crystal X-ray diffraction. The title material crystallizes in the triclinic space group P-1 with a = 6.4170(3) , b = 9.4510(2) , c = 10.9350(3) , a = 115.240(2)^o, b = 80.190(3)^o and g = 106.810(2)⁰. The structure presents a centro-symmetrical clusters Co₄P₄O₂₈ consists of two Co₂O₁₁ units and two P₂O₇ pyrophosphate groups. The junction between clusters is assured by two P₂O₇ groups to form a three-dimensional anionic framework having different interconnecting tunnels running along [100] and [010]. The former contains the Na⁺ and Ag⁺ cations. The conductivity measurements of (Na_0.71Ag_0.29)₂CoP₂O₇ are studied over a temperature interval from 783 to 903 K using the frequency response analyzer with 0.5 V amplitude signal over the range of 13 MHz - 5 Hz.