Abstract The modulation of cosmic rays by a propagating plasma disturbance, a global merged interaction region (GMIR), in the heliosheath is simulated using a Vlasov–Fokker–Planck equation for the transport of energetic particles with significant anisotropy. The prescribed plasma structure of the GMIR contains a shock front and plasma rarefaction region behind the shock, which propagate through a simplified paramagnetic shielding model of the heliosheath. When a GMIR goes through the heliospheric magnetic field in the inner heliosheath, its modulation effects on cosmic rays are consistent with typical Forbush decreases. When a GMIR goes through the interstellar magnetic field in the outer heliosheath, only cosmic rays with large pitch angles with respect to the magnetic field vector (cosine values close to zero) are modulated by it. The difference is due to the very weak scattering of particles by the interstellar turbulence. Particles trapped in the rarefied magnetic field inside a GMIR suffer a significant amount of adiabatic cooling, which results in a considerable intensity decrease and a bidirectional anisotropy. The simulation result can be used to explain what Voyager 1 observed in the very local interstellar medium. Depending on the strength of plasma compression inside a GMIR, some cosmic rays may be accelerated, but the GMIR effect on the cosmic-ray intensity is much weaker than that due to adiabatic cooling because particles have only a brief interaction with a GMIR without trapping.