We demonstrate that global observations of high-energy cosmic rays contribute to understanding unique characteristics of a large-scale magnetic flux rope (MFR) causing a magnetic storm in August 2018. Following a weak interplanetary shock on 25 August 2018, a MFR caused an unexpectedly large geomagnetic storm. It is likely that this event became geoeffective because the MFR was accompanied by a corotating interaction region (CIR) and compressed by high-speed solar wind following the MFR. In fact, a Forbush decrease was observed in cosmic-ray data inside the MFR as expected, and a significant cosmic-ray density increase exceeding the unmodulated level before the shock was also observed near the trailing edge of the MFR. The cosmic-ray density increase can be interpreted in terms of the adiabatic heating of cosmic rays near the trailing edge of the MFR, as the corotating interaction region prevents free expansion of the MFR and results in the compression near the trailing edge. A northeast-directed spatial gradient in the cosmic-ray density was also derived during the cosmic-ray density increase, suggesting that the center of the heating near the trailing edge is located northeast of Earth. The second order anisotropy is observed during the density increase clearly representing an intensity enhancement of cosmic rays with approximately 90 degree pitch angle, possibly indicating the betatron acceleration of CRs during the cosmic-ray density increase and/or accelerated CRs leaking along the magnetic field from the density increase region toward the south where lower CR population is expected. This is one of the best examples demonstrating that the observation of high ­energy cosmic rays provides us with information of the three-dimensional macroscopic picture of the interaction between coronal mass ejections and the ambient solar wind, which is essential for prediction of large magnetic storms.