•We demonstrate quasi-heteroepitaxy of β-Ga2O3 by the halide vapor phase epitaxy.•Ultra-high-growth rate over 250 μm/h is achieved.•Orientation of the β-Ga2O3 films is controlled by off-angled sapphire substrates.•With the off-angle increase, one of the in-plane orientations is strongly favored.•In combination with thick film growth, quasi-heteroepitaxial layers are achieved.We demonstrate the high-speed growth of β-Ga2O3 quasi-heteroepilayers on off-angled sapphire (0 0 0 1) substrates by halide vapor phase epitaxy (HVPE). (2¯01) oriented β-Ga2O3 layers were successfully grown using GaCl and O2 as source gases. The growth rate monotonically increased with increasing the partial pressures of the source gases, reaching over 250 μm/h. This rate is over two orders of magnitude larger than those of conventional vapor phase epitaxial growth techniques such as molecular beam epitaxy or metalorganic vapor phase epitaxy. X-ray pole figure measurements indicated the presence of six in-plane rotational domains, in accordance with the substrate symmetry, plus some minor (3 1 0) domains. By the use of off-angled substrates and thick layer overgrowth, one of the in-plane orientations was strongly favored and the (3 1 0) residuals effectively suppressed, so that quasi-heteroepitaxial growth was achieved. Therefore, these results indicate the high-potential of the HVPE technique for the growth of thick and thin β-Ga2O3 layers for the cost-effective production of β-Ga2O3 based devices.