The properties of Iconel 718 determine its application for parts operating in extremely tough conditions. The difficulties when machining nickel-based superalloys allowed in recent years for researching other machining methods. One of the proposed methods is Wire Electrical Discharge Machining (WEDM). It becomes possible to minimize or eliminate such problems associated with electrical discharge machining as microcracks, forming of a white layer, or high surface roughness. One way to avoid these issues is to apply finishing machining. The literature indicates that the peak current is the main parameter responsible for shaping the machined surface in finishing WEDM. Furthermore, few works focus on the electrode’s infeed, in particular there are not many papers regarding the influence of the infeed on the machined surface parameters. Therefore, the paper aims to investigate on the influence of the peak current and infeed during finishing WEDM on the surface properties of Inconel 718. The paper presents measurements of selected surface topography parameters and Abbot Firestone curves (AFC). The presented plots allowed to determine the ranges of the process parameters for which the lowest surface roughness values were achieved. Cross-sections were performed to measure the thickness of a white layer. Nanohardness HV0,01 measured by Berkovich tip was recorded to determine the size of a heat affected zone (HAZ). The correlation between the peak current Ic and the infeed z regarding the machined surface quality was presented.