The present invention concerns a reactor for the conversion of carbon dioxide or carbon monoxide into hydrocarbon and/or alcohol comprising a support made from an electrically and thermally conductive material, forming the wall or walls of at least one longitudinal channel that passes through the support and also acting as the cathode of the reactor, at least one wire electrode forming an anode of the reactor, and extending within each longitudinal channel, and being arranged at a distance from the wall or walls of the longitudinal channel, each wire electrode optionally being covered with an electrically insulating layer along the part of the wire electrode extending within the longitudinal channel, a catalyst capable of catalysing a conversion reaction for the conversion of carbon dioxide or carbon monoxide into hydrocarbon and/or alcohol, the catalyst being situated between the wire electrode and the wall or walls of each longitudinal channel.