In this work, we have performed molecular dynamics simulations of a nucleation process of an SWNT from a catalytic metal cluster inside a carbon nanotube template to gain understanding in the growth mechanism. As an initial condition, a metal cluster with dissolved carbon atoms was placed in a rigid carbon nanotube. By supplying carbon atoms to the metal-carbide, nucleation process of the inner SWNT was observed. Once the open surface of the metal cluster is covered with carbon atoms, the carbon feeds are adsorbed onto metal atoms adjacent to the outer-tube wall. Then the supersaturated carbon atoms on the metal-carbide cluster surface lifts of and the cap can be recognized together with the tubular structure. The formation of the inner SWNT was confirmed for various metal-cluster sizes and outer-tube diameters, where the morphology depends on the outer-tube diameter due to the curvature variation. The distance between the inner and outer nanotubes is determined by the layered structure of the metal-carbide and is insensitive to the outer nanotube chirality.