This work focuses on the development of a novel electrochemical sensor for the determination of morphine in the presence of diclofenac. The facile synthesis of graphene-Co3O4 nanocomposite was performed. The prepared material (graphene-Co3O4 nanocomposite) was analyzed by diverse microscopic and spectroscopic approaches for its crystallinity, composition, and morphology. Concerning the electrochemical determinations, after drop-casting the as-fabricated graphene-Co3O4 nanocomposite on the surface of a screen-printed graphite electrode (SPGE), their electrochemical performance was scrutinized towards the morphine detection. It was also found that an SPGE modified by a graphene-Co3O4 nanocomposite exhibited better electrocatalytic activity for morphine oxidation than unmodified electrode. Under optimal conditions, the differential pulse voltammetry (DPV) was employed to explore the present sensor (graphene-Co3O4/SPGE), the findings of which revealed a linear dynamic range as broad as 0.02–575.0 µM and a limit of detection (LOD) as narrow as 0.007 μM. The sensitivity was estimated to be 0.4 µM/(µA cm2). Furthermore, the graphene-Co3O4/SPGE sensor demonstrated good analytical efficiency for sensing morphine in the presence of diclofenac in well-spaced anodic peaks. According to the DPV results, this sensor displayed two distinct peaks for the oxidation of morphine and diclofenac with 350 mV potential difference. In addition, the graphene-Co3O4/SPGE was explored for voltammetric determination of diclofenac and morphine in pharmaceutical and biological specimens of morphine ampoule, diclofenac tablet, and urine, where recovery rates close to 100% were recorded for all of the samples.