First-order branched tree structures of MoO3 belts on sillimanite fibers (refractor wool) were grown by a vapor transport method. At longer growth times, MoO3 micro-belts on micro-belts form a flower-like structure. Most belts are of alpha-MoO3, and they grow in the two opposite directions along the c-axis. They show a high level of crystal quality, clean surfaces, sharp edges, and a triangular-shape tip with certain angles. The most frequent are angles of 47 degrees and 94 degrees. The growth mechanism is of vapor-solid type. In the initial stages of growth, elements specific for spontaneous spread and island formation on the surface of the sillimanite fibers described in the literature are observed. Significant enhancement of the thickness suggests that a layer-by-layer 2D growth is also probable. It is thought that responsible for such growth is direct vapor deposition of the Mo-O vapors on the already formed belts, this being similar to thin film growth. Curved surfaces of the substrate (in our case of the sillimanite fibers), on which the MoO3 belts are growing, are important and can be used for the directional growth control of the belts and formation of hierarchical structures. The vapor transport method allows the formation of beta-MoO3 belts that grow in the b-axis direction.