In order to create strong composite materials, a good dispersion of carbon nanotubes (CNTs) and nanofibers (CNFs) in a matrix material must be obtained. We proposed a simple method of growing the desirable carbon nanomaterial directly on the surface of matrix particles. CNTs and CNFs were synthesised on the surface of model object, silica fume particles impregnated by iron salt, and directly on pristine cement particles, naturally containing iron oxide. Acetylene was successfully utilised as a carbon source in the temperature range from 550 to 750 °C. 5-10 walled CNTs with diameters of 10-15nm at 600 °C and 12-20nm at 750 °C were synthesised on silica particles. In case of cement particles, mainly CNFs with a diameter of around 30nm were grown. It was shown that high temperatures caused chemical and physical transformation of cement particles.