High-resolution transmission electron microscopy (HRTEM) was employed to study the nucleation and subsequent growth mechanism of crystalline diamond grown on copper TEM grids by the hot-filament chemical vapour deposition process. The HRTEM revealed direct evidence for the formation of a diamond-like amorphous carbon layer 8-14 nm thick, in which small diamond microcrystallites about 2-5 nm across were embedded. These diamond microcrystallites were formed as a result of direct transformation of the diamond-like carbon into diamond. Large diamond crystallites were observed to grow from these microcrystallites. The diamond surface was found to be non-uniform. It is envisaged that the diamond microcrystallites present in the amorphous, diamond-like carbon layer provide nucleation sites on which the large diamond crystallites grew. A mechanism of diamond growth has been proposed, based on the experimental findings, and is consistent with available theoretical models and numerous experimental observations reported in the literature.