We experimentally investigated a "molecular-linear-motor" system consisting of a capsule-like carbon nanotube (CNT) in the interior space of a host CNT. Transmission electron microscopy revealed the capsule traveled back and forth between both ends of the hollow space along the axial direction and rotated simultaneously. The mechanism was well explained with molecular dynamics simulation by considering the driving force supplied from thermal energy. The present system operates around room temperature and this opens up the possibility of designing novel nanodevices such as oscillators and switching memory devices.