© 2018, Springer Science+Business Media, LLC, part of Springer Nature.Structural, morphological and optical properties of prepared CuS nanostructures were analyzed using XRD, SEM, FTIR, UV–Vis and DRS methods. Experimental results indicated that samples show good crystalline structures. In addition, the particles size and their morphology changed with pH value. UV–Vis absorption shifts to blue by variation of pH and also both the diffuse reflectance and optical absorption of CuS nanostructures have absorption regions of 300–400 nm, respectively. Electrical characteristics of these structures were also investigated in the frequency range of 2 kHz–1 MHz by using impedance–voltage (Z–V) measurements. Experimental results showed that both the value of capacitance (C) and conductance (G/ω) are strong functions of frequency and voltage especially in depletion and accumulation regions due to the effects of surface states (Nss), series resistance (Rs) and interfacial (CuS–PVA) polymer layer. G/ω–V plot revealed a distinctive peak for each frequency in depletion layer and peak positions shift towards to accumulation region with increasing frequency. The voltage dependent profile of the Nss was found from the high–low capacitance (CLF–CHF) and Hill–Coleman methods and obtained values are agreeing with each other. The voltage dependent profile of Rs was also obtained using the Nicollian–Brews method and it decreases with increasing frequency. The obtained mean value of Nss was found at about 2 × 1011 eV−1 cm−2, which is lower and reasonable for an electronic device. Obtained lower values of Nss can be attributed to the passivation effect of the (CuS–PVA) polymer layer.