Observations from multiple spacecraft show that there are energy spectral “breaks” at 1–10 MeV in some large CME-driven shocks. However, numerical models can hardly simulate this property due to high computational expense. The present paper focuses on analyzing these energy spectral “breaks” by Monte Carlo particle simulations of an isolated CME-driven shock. Taking the 2006 Dec 14 CME-driven shock as an example, we investigate the formation of this energy spectral property. For this purpose, we apply different values for the scattering time in our isolated shock model to obtain the highest energy “tails,” which can potentially exceed the “break” energy range. However, we have not found the highest energy “tails” beyond the “break” energy range, but instead find that the highest energy “tails” reach saturation near the range of energy at 5 MeV. So, we believe that there exists an energy spectral “cut off” in an isolated shock. If there is no interaction with another shock, there would not be formation of the energy spectral “break” property.

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