Electron energy-loss spectroscopy (EELS) is a unique tool that is extensively used to investigate the plasmonic response of metallic nanostructures. We present here a novel approach for EELS calculations using the finite-difference time-domain (FDTD) method (EELS-FDTD). We benchmark our approach by direct comparison with results from the well-established boundary element method (BEM) and published experimental results. In particular, we compute EELS spectra for spherical nanoparticles, nanoparticle dimers, nanodisks supported by various substrates, and a gold bowtie antenna on a silicon nitride substrate. Our EELS-FDTD method can be easily extended to more complex geometries and configurations. This implementation can also be directly exported beyond the FDTD framework and implemented in other Maxwell's equation solvers.