Photodetachment of hydrogen negative ion near a dielectric sphere has been studied by using the image method combined with the semiclassical closed orbit theory. Firstly, we analyze the image charge distribution of the detached electron near the dielectric sphere; then we put forward the Hamiltonian for this system. By solving the Hamiltonian canonical equations, we can find the closed orbits of the detached electrons moving near the dielectric sphere. With the help of the semiclassical closed orbit theory, we derive the formula for calculating the photodetachment cross section of this system. Then we can calculate and analyze the photodetachment cross section. Calculated results suggest that the photodetachment cross section of the hydrogen negative ion near a dielectric sphere is not only related to the photon energy, but also the dielectric constant of the sphere. For a given dielectric sphere, with the increase of photon energy, the oscillating amplitude in the photodetachment cross section decreases while the oscillation frequency increases. When the photon energy is increased to a critical value, the oscillating structures in the cross section disappear. In addition, with the increase in the dielectric constant of the dielectric sphere, the oscillating structure in the photodetachment cross section becomes much more complicated. When the dielectric constant is increased to infinity, the photodetachment cross section of this system is consistent with the photodetachment cross section of the hydrogen negative ion near a metal sphere. Therefore, we can control the photodetachment cross section of the hydrogen negative ion near a dielectric sphere by changing the photon energy and the dielectric constant. Our study may provide some theoretical guidance and reference values for the experimental research of photodetachment of negative ion near the dielectric sphere.