Graphene is a two-dimensional material with unique physical and chemical properties, whose excellent biocompatibility has also attracted widespread attention in the field of biosensing and medical detection. Graphene provides a novel solution for dramatically improving the sensitivity of terahertz metasurface sensors, since the electrical conductivity can be modified by contact with biomolecules. In this paper, a metal-graphene hybrid metasurface is proposed and demonstrated for high-sensitive nortriptyline sensing based on the plasmon-induced transparency (PIT) resonances. The π-π stacks between nortriptyline and graphene lead to an increase in the Fermi level of graphene and a decrease in the conductivity, thus enhancing the PIT resonance. Experimental results show that the peak-to-peak amplitude magnitude of the PIT window is enhanced up to 3.4-fold with 1 ng nortriptyline analyte, and the minimum detection limit is extended down to 0.1 ng. But no significant change is observed from the samples without graphene as a comparative experiment, which demonstrates that the presence of graphene greatly enhances the bonding to the drug molecules and improves the sensing sensitivity. This metasurface sensor has the advantages of high sensitivity, fast detection speed, label-free and steady properties, which has potential applications in the fields of trace molecular sensing and disease diagnosis.