Multicomponent MWCNT-added glasses of the [(Cu5Se75Te10In10)100−x(CNT)x] (x = 0, 1, and 2) system have been developed by a cost-effective melt-quench method that is also known for its convenience. Structural properties have been studied using XRD and FESEM. Differential Scanning Calorimetry scan has been done at a heating rate of 10 K/min which also confirms the glassy nature of the as-prepared and MWCNT-added Cu5Se75Te10In10 composite. The effect of CNTs on transition temperatures, thermal characteristics such as thermal stability and Glass-forming stability has been discussed. The variations of dielectric relaxation of this new composite with temperature and frequency have been investigated from room temperature up to 373 K and frequency regime from 1 Hz to 1 MHz. Moreover, it is also observed that dielectric constant and dielectric loss reduces sharply at the high-frequency side but increases with increase in CNT concentration as well as temperature. The highest dielectric constant value (2000) for 2 wt% MWCNT/Cu5Se75Te10In10 at low temperatures and the low-frequency regime is approximately ten times greater than the host glassy composite Cu5Se75Te10In10 was observed.