Heat conduction of a real quasi-one dimensional material, the finite length carbon nanowire (CNW), inserted into the single-walled carbon nanotube (SWNT) has been studied by the molecular dynamical (MD) method, in which both of the longitudinal as well as transverse motions of the chain atoms in the SWNT have been permitted. It is found that the thermal conductivity $kappa $ of the carbon nanowire is very high at room temperature, and diverges more likely with the chain length logarithmically.