Based on comparative observations with the conducting atomic force microscope and the scanning tunneling microscope，conductance enhancement phenomenon of graphene ribbons on highly oriented pyrolytic graphite surfaces has been studied. According to measured data of local resistance on the samples，the phenomenon is attributed to the state of point contact of the conducting tip on the sample surface. It was demonstrated that the conductance of the point contact is proportional to the local density of electrons in the contacting surface area，so we conclude that the conductance enhancement phenomenon results from the high density of electrons on the graphene ribbons.