Structural change of a multiwall carbon nanotube (MWNT) contacted with a molybdenum (Mo) electrode during Joule heating and its electrical conducting properties were investigated by in situ transmission electron microscopy. We found that inner shells of the MWNT were retracted (slide and disappeared) to the Mo electrode, and the total electrical conductance decreased accordingly. This result shows that inner shells being retracted to the Mo electrode contribute to the electric conduction in the MWNT. Utilizing this inner-shell retraction phenomenon, inter-shell conductance per unit length in a MWNT is derived to be ca. 13-19 mS/μm.