A simple fabrication route for an all-solid-state carbon paste Cu(II)-selective potentiometric sensor on the basis of composite sensing layer consisting of PbS microparticles, graphite (G), multi-walled carbon nanotube, and paraffin oil has been propounded. Optimization studies for sensing composite layer signified that the composite contained 10 mg PbS, 10 mg MWCNT, 60 mg G, and 20 mg PO exposed the most promising potentiometric performance properties. The sensor displayed a stable and selective linear response to Cu(II) ions in the concentration range of 1.0 × 10−6–1.0 × 10−2 M (R2 = 0.9992) with an average potential change of 30.2 mV/decade. Detection limit, response time, and life-span of the sensor were determined as 5.0 × 10−7 M, 15 s, and 3 weeks, respectively. The fabricated sensor was successfully used in practical applications, serving as an indicator electrode to determine the end-point of Cu(II) titrations and to measure Cu(II) content in Cu(II)-spiked tap water samples.