We study the photodetachment of H$^−$ ion in crossed gradient electric and magnetic fields and put forward an analytical formula for calculating the photodetachment cross-section. Compared to the photodetachmentof H$^−$ ion in a gradient electric field, the Hamiltonian of the detached electron has three degrees of freedom, which makes the dynamical behaviour of the detached electron complex. Photodetachment cross-section for variousexternal fields and the laser polarization are calculated and displayed. A comparison with the photodetachment cross-section in crossed uniform electric and magnetic fields or in a single gradient electric field has been made.The agreement of our results with the above two special cases suggests the correctness of our calculation. Our study may have some potential applications in the photodetachment microscopy experiment or in ion detection.