We studied kinetic roughening of copper surfaces electrochemically dissolved at constant current densities by atomic force microscopy. The surface was found to roughen with time and the surface width increased with the length scale with the roughness exponent α of [Formula Presented] in the stationary state. This value is different from that in electrochemical deposition, 0.87, under the stable growth condition [A. Iwamoto et al., Phys. Rev. Lett. 72, 4025 (1994)]. The observed roughening in the dissolution process is discussed in terms of nonlocal effects.