Abstract We report on the energy dependence of Galactic cosmic rays (GCRs) in the very local interstellar medium (VLISM) as measured by the Low Energy Charged Particle (LECP) instrument on the Voyager 1 spacecraft. The LECP instrument includes a dual-ended solid-state detector particle telescope mechanically scanning through 360° across eight equally spaced angular sectors. As reported previously, LECP measurements showed a dramatic increase in GCR intensities for all sectors of the ≥211 MeV count rate (CH31) at the Voyager 1 heliopause (HP) crossing in 2012; however, since then the count rate data have demonstrated systematic episodes of intensity decrease for particles around 90° pitch angle. To shed light on the energy dependence of these GCR anisotropies over a wide range of energies, we use Voyager 1 LECP count rate and pulse height analyzer (PHA) data from ≥211 MeV channel together with lower-energy LECP channels. Our analysis shows that, while GCR anisotropies are present over a wide range of energies, there is a decreasing trend in the amplitude of second-order anisotropy with increasing energy during anisotropy episodes. A stronger pitch angle scattering at higher velocities is argued as a potential cause for this energy dependence. A possible cause for this velocity dependence arising from weak rigidity dependence of the scattering mean free path and resulting velocity-dominated scattering rate is discussed. This interpretation is consistent with a recently reported lack of corresponding GCR electron anisotropies.