We present an analysis of the bandwidth of an asymmetric 8-beam Fourier grating as the beam multiplexer for a 4.7 THz local oscillator used in a heterodyne receiver. We take the grating designed for NASA GUSTO balloon observatory as an example to address the bandwidth question although it does not need to operate over a wide frequency range. By illuminating the grating at different frequencies from 4.445 to 5.045 THz, we simulated the changes of its performance in three aspects using COMSOL Multiphysics: diffraction efficiency, power uniformity, and the angular distribution of the output beams. These parameters can affect the coupling efficiency between the output beams of the grating and the beams of a mixer array. The bandwidth of the grating is found to be 230 GHz, corresponding to 4.9% of the operating frequency, which is sufficient for many applications.