The electron-phonon interaction (EPI) is instrumental in a wide variety of phenomena in solid-state physics, such as electrical resistivity in metals, carrier mobility, optical transition, and polaron effects in semiconductors, lifetime of hot carriers, transition temperature in BCS superconductors, and even spin relaxation in diamond nitrogen-vacancy centers for quantum information processing. However, due to the weak EPI strength, most phenomena have focused on electronic properties rather than on phonon properties. One prominent exception is the Kohn anomaly, where phonon softening can emerge when the phonon wave vector nests the Fermi surface of metals. Here we report a new class of Kohn anomaly in a topological Weyl semimetal (WSM), predicted by field-theoretical calculations, and experimentally observed through inelastic x-ray and neutron scattering on WSM tantalum phosphide. Compared to the conventional Kohn anomaly, the Fermi surface in a WSM exhibits multiple topological singularities of Weyl nodes, leading to a distinct nesting condition with chiral selection, a power-law divergence, and non-negligible dynamical effects. Our work brings the concept of the Kohn anomaly into WSMs and sheds light on elucidating the EPI mechanism in emergent topological materials.