The total photodetachment cross section of a negative ion near a repulsive center is studied based on the closed-orbit theory. An analytical expression, written as a product of the zero-field photodetachment cross section and a modulation function, is obtained for energy above and below threshold. The expression also incorporates the different wave sources produced by different negative ions. The present results are shown to be accurate by comparing with quantum calculations based on the exact Coulomb Green's function. We also compared the photodetachment cross section near a repulsive center with that in a homogeneous electric field and found interesting connections between the two.