Inelastic neutron-scattering (INS) experiments were performed to investigate the spin dynamics in magnetoelectric effect LiCoPO4 single crystals. Weak dispersion was detected in the magnetic excitation spectra along the three principal crystallographic axes measured around the (0 1 0) magnetic reflection. Analysis of the data using linear spin-wave theory indicates that single-ion anisotropy in LiCoPO4 is as important as the strongest nearest-neighbor exchange coupling. Our results suggest that Co2+ single-ion anisotropy plays an important role in the spin dynamics of LiCoPO4 and must be taken into account in understanding its physical properties. High-resolution INS measurements reveal an anomalous low-energy excitation that we hypothesize may be related to the magnetoelectric effect of LiCoPO4.