By means of momentum-resolved electron energy loss spectroscopy (EELS) coupled with scanning transmission electron microscopy, we have studied the dispersion relation of interband plasmonic modes in the ultraviolet in black phosphorus. We find that the dispersion of the interband plasmons is anisotropic. Experimental results are reproduced by density functional theory, by taking into account both the anisotropy of the single-particle response function, arising from the anisotropic band structure, and the damping. Moreover, our theoretical model also indicates the presence of low-energy excitations in the near-infrared that are selectively active in the armchair direction, whose existence has been experimentally validated by high-resolution EELS (HREELS) in reflection mode. \ 2018 The Royal Society of Chemistry.