Understanding electron transfer (ET) from a single molecule to another single molecule holds essential importance to realize bottom-up molecular devices in which constituent molecules are self-assembled via noncovalent interactions between each other. However, rather little is currently known about the ET properties at the single-molecule interface. Here we employ molecular tips to quantify the ET through a H-bond between single molecules. We found that a H-bond conducts electrons better than a covalent sigma bond at short-range. Its conductance, however, decays steeply as the chain length of the H-bonded molecules increases. First-principle calculations were performed to reveal the electronic origin of the facile ET through the H-bond. Our results demonstrate that H-bonding in a molecular junction significantly affects its transport property.