An embodiment of a process for manufacturing a semiconductor power device envisages the steps of: providing a body made of semiconductor material having a first top surface; forming an active region with a first type of conductivity in the proximity of the first top surface and inside an active portion of the body; and forming an edge-termination structure. The edge-termination structure is formed by: a ring region having the first type of conductivity and a first doping level, set within a peripheral edge portion of the body and electrically connected to the active region; and a guard region, having the first type of conductivity and a second doping level, higher than the first doping level, set in the proximity of the first top surface and connecting the active region to the ring region. The process further envisages the steps of: forming a surface layer having the first type of conductivity on the first top surface, also at the peripheral edge portion, in contact with the guard region; and etching the surface layer in order to remove it above the edge portion in such a manner that the etch terminates inside the guard region.