The transport properties of solid composite electrolytes (1 – x)LiClO4–xCND (where СND are “UDA-S” nanodispersed diamonds with a specific surface area Ssp = 300 ± 20 m2/g, 0 < x < 1) are studied. It is found that an addition of CND leads to an increase of the composite conductivity (σ) by 3–5 orders of magnitude to 8 × 10–4 S/cm at T = 100°C at x = 0.9. The experimental data in the concentration range 0.1 < x < 0.8 at the temperatures of 50–200°C are described by the theoretical dependences, which ore obtained using the modified mixing equation. Using the method of cycling voltammetry in the E/0.2LiClO4–0.8CND/E cells (where E is Ag, Cu, Ni, and graphite), it is shown that this composite solid electrolyte is electrochemically stable in the voltage range up to 3.5 V. By the examples of solid-state supercapacitor C/0.2LiClO4–0.8CND/C and solid-state lithium-ion battery LiMn2O4/0.2LiClO4–0.8CND/LiMn2O4, it is shown that, in principle, the composite solid electrolytes with the nanodiamond additives can be used in the electrochemical devices. Thus, it is demonstrated that nanodispersed diamonds can be considered as an effective non-oxide additive in the composite solid electrolytes based on lithium perchlorate.