This work reports the first implementation of potentiometric solid-contact ion-selective electrodes (SC-ISEs) using the nanocomposite of ordered bimetallic AuCu nanoparticles coupled with multi-walled carbon nanotubes (oAuCuNPs-MWCNTs) as transducers. The unexplored nanocomposite oAuCuNPs-MWCNTs is deposited by solvent casting on gold sputtered copper electrodes as an intermediate layer and then covered with ion-selective membranes to form potentiometric sensors. The performance of the sensors is evaluated by determining Ca2+ and SO42− as an example of cation and anion, respectively. The obtained electrodes show response slopes of 29.0 mV/decade for Ca2+-selective SC-ISEs from 10−6 to 10−1 M, and −27.0 mV/decade for SO42--selective SC-ISEs from 10−5 to 10−1 M. Moreover, they exhibit high double layer capacitance (54 μF for Ca2+-selective SC-ISEs and 105 μF for SO42--selective SC-ISEs), fast charge transfer (resistance of 2.22 MΩ for Ca2+-selective SC-ISEs and 0.46 MΩ for SO42--selective SC-ISEs) and low potential drift (15 ± 3 μV/h for Ca2+-selective SC-ISEs and 118 ± 16 μV/h for SO42--selective SC-ISEs over 12 h). Additionally, none of the redox reactions, light interference and water films is observed. These results indicate that the combination of bimetallic nanoparticles and carbon nanomaterials offers great promise for the development of more robust and useful electrochemical sensors.