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.