The transition dipole of the hyperfine-rotation spectrum of J = 1←0 within the vibronic ground (X¹Σ, v = 0) state of BrF molecule is derived, and thus, the transition selection rules are summarized as follows: ΔJ = ±1; ΔF₁ = 0, ±1 and ΔF = 0, ±1, and those of ΔF₁ = ΔF are intense while those of ΔF₁ ≠ ΔF are weak. Some spectral lines result from both the electric dipole transition and nuclear magnetic dipole transition due to perturbations, however, the magnetic dipole transition only contributes about one-billionth in the spectral intensity. The spectral linewidth is determined to be about 18 kHz by calculating the spectral transition probability. The obtained spectral linewidth and relative intensities are consistent with the experimental results. Additionally, the hyperfine-rotation spectral positions are determined by diagonalizing the Hamiltonian matrix in the basis of |JI₁F₁I₂F\rangle , which is also in good agreement with the experiments within 10^–8 (one-fiftieth of the spectral line width). Hence, the microwave hyperfine-rotation spectrum is simulated. In addition, we find that the nuclear spin-spin interaction not only slightly shifts the hyperfine-rotation spectral positions but also changes the sequence of the spectra. As to those unavailable constants of molecules, the fairly precise molecular constants can be achieved by quantum chemical calculation, say, by employing MOLPRO program, and then the simulated spectra can guide the spectral assignment. Besides the guidance of spectral assignment, our results are also helpful for other relevant applications such as in absolute single quantum state preparation.