Thermal boundary conductance (TBC) is important for heat dissipation in light-emitting diodes (LEDs). In this study, we predicted the TBC between the high thermal conductivity boron arsenide (BAs) and silicon (Si) by nonequilibrium molecular dynamics (MD) simulations. From the thermal conductivity accumulation function with respect to phonon frequency, the dominant phonon frequencies for heat conduction in BAs are extremely different from those in Si. However, our nonequilibrium MD simulations indicated that the TBC of the BAs/Si interface was still high compared to most other interfaces, even though there was a major frequency mismatch in the thermal conductivity accumulation function between BAs and Si. The primary reason for the high TBC is the overlap of phonon density of states between BAs and Si in the frequency range of 5–8 THz. The range of predicted TBC of the BAs/Si interface was between 200 and 300 MW/m2 K in the temperature range of 300–700 K, and the values of the TBC were not sensitive to the temperature. We also found that the TBCs in Si/BAs and Si/Ge interfaces were close to each other considering the simulation uncertainty. This work indicates BAs as an excellent material for heat dissipation across the interfaces.