We present experimental and theoretical results on photodetachment of Br(-) and F(-) in a strong infrared laser field. The observed photoelectron spectra of Br(-) exhibit a high-energy plateau along the laser polarization direction, which is identified as being due to the rescattering effect. The shape and the extension of the plateau is found to be influenced by the depletion of negative ions during the interaction with the laser pulse. Our findings represent the first observation of electron rescattering in above-threshold photodetachment of an atomic system with a short-range potential.