We report measurements of the magnetic excitation spectrum of the layered antiferromagnet La₂CoO₄ by time-of-flight neutron inelastic scattering. In the energy range probed in our experiments (0–250 meV) the magnetic spectrum consists of spin-wave modes with strong in-plane dispersion extending up to 60 meV, and a nearly dispersionless peak at 190 meV. The spin-wave modes exhibit a small (∼1 meV) dispersion along the magnetic zone boundary. We show that the magnetic spectrum can be described very well by a model of a Heisenberg antiferromagnet that includes the full spin and orbital degrees of freedom of Co²⁺ in an axially distorted crystal field. The collective magnetic dynamics are found to be controlled by dominant nearest-neighbor exchange interactions, strong XY-like single-ion anisotropy and a substantial unquenched orbital angular momentum.