Nodal-line semimetals (NLSMs), a large family of new topological phases of matter with continuous linear band crossing points in the momentum space, attract considerable attention. Here, we report the direct observation of plasmons originating from topological nodal-line states in a prototypical NLSM ZrSiS by high-resolution electron energy loss spectroscopy. There exist three temperature-independent plasmons with energies ranging from the near- to the mid-infrared frequencies. With first-principles calculations of a slab model, these plasmons can be ascribed to the correlations of electrons in the bulk nodal lines and their projected surface states, dubbed nodal-line plasmons. An anomalous surface plasmon has higher excitation energy than the bulk plasmon due to the larger contribution from the nodal-line projected surface states. This work reveals the novel plasmons related to the unique nodal-line states in a NLSM.