During a few solar energetic particle (SEP) events, solar protons were trapped within the geomagnetic field and reached the outer edge of the inner radiation belt. We reproduced this phenomenon by modeling the proton flux distribution at the Low-Earth Orbit (LEO) for different geomagnetic conditions during solar particle events. We developed a three-dimensional relativistic test particle simulation code to compute the 70–180 MeV solar proton Lorentz trajectories in low L-shell range from 1 to 3. The Tsyganenko model (T01) generated the background static magnetic field with the IGRF (v12) model. We have selected three Dst index values: −7, −150, and −210 nT, to define quiet time, strong, and severe geomagnetic storms and to generate the corresponding inner magnetic field configurations. Our results showed that the simulated solar proton flux was more enhanced in the high-latitude regions and more expanded toward the lower latitude range as long as the geomagnetic storm was intensified. Satellite observations and geomagnetic cutoff rigidities confirmed the numerical results. Furthermore, the LEO proton flux distribution was deformed, so the structure of the proton flux inside the South Atlantic Anomaly (SAA) became longitudinally extended as the Dst index decreased. Moreover, we have assessed the corresponding radiation environment of the LEO mission. We realized that, for a higher inclined LEO mission during an intense geomagnetic storm (Dst = −210 nT), the probability of the occurrence of the Single Event Upset (SEU) rates increased by 19\% and the estimated accumulated absorbed radiation doses increased by 17\% in comparison with quiet conditions.