Discrete catalytic nanoparticles with diameters in the range of 1-3 nm are obtained by placing controllable numbers of metal atoms into the cores of apoferritin. With nanoparticles placed on transmission electron microscope (TEM) grids coated with ultra-thin alumina membranes, isolated single-walled carbon nanotubes are grown by chemical vapor deposition and directly examined by TEM. The characterizations, carried out at single-tube and single-particle level, obtain clear evidence that the diameters of the nanotubes are determined by the diameters of catalytic nanoparticles. For the first time, both ends of an as-grown single-walled nanotube are imaged by TEM, leading to a microscopic picture of the nanotube-growth mechanism.