In the current investigation, we report successful synthesis of well-crystalline Cd-doped ZnO nanostructures above their miscibility range (Zn$_{1-{x}}$Cd$_x$O, $x$ = 0.1, 0.2, 0.3, and 0.4) via an easy and simple low-temperature solution method. The as-prepared samples were studied for their structural, optical and electrical behaviour as a function of Cd doping. The X-ray diffraction reveals that the as-prepared samples possess a pure hexagonal wurtzite structure of ZnO without any essence formation of a separate CdO phase up to 30% of Cd doping. However, on increasing the Cd concentration i.e.,>30%, clustering of CdO (as a separate phase) is visible in X-ray pattern. Ultraviolet–visible (UV–Vis) spectra show the effective change in the optical band gap with increase in Cd doping. Zn–O stretching modes of vibrations are confirmed by Fourier transform infrared spectroscopy in all samples. The frequency-dependence behaviour of dielectric constant, dielectric loss and ac conductivity of as-prepared samples were studied at room temperature. The colossal dielectric response is found to be ${\sim}$6${\times}$10$^3$ at 1 kHz for Cd-doped samples. The observed dielectric behaviour is explained on the basis of Maxwell–Wagner model and Koops phenomenological approach.