We have implemented the solid-on-solid (SOS) kinetic model in the framework of electrochemistry to study the evolution of surface morphology during driven metal dissolution. Our results show that the surface roughens with increasing applied electrical potential, as demonstrated by the increase of the interface width and of the surface high-frequency-power spectrum. An abrupt change on the roughness is observed at a certain value of the applied potential, which indicates the possibility of an electrochemically driven kinetic-roughening transition. A change in the dissolution mechanism is proposed from a regime of kink propagation at steps to a situation where low-coordination sites participate just as actively in the dissolution process.