Al4SiC4 is a refractory ceramic with a reported band gap of about 2.5 eV, making it an interesting semiconductor material for various applications in the field of energy. However, the synthesis of Al4SiC4 single crystals has so far not been investigated. In this study, the sublimation growth method is explored as a potential route for getting high quality single crystals. Combining a thermodynamic analysis with an extensive experimental approach, the vaporization and condensation phenomena in the Al4C3-SiC system are described. Experimental conditions, such as initial composition, baking temperature and temperature gradient, are investigated and demonstrated regarding the crystallization of Al4SiC4. From the results obtained, a condensed phase diagram at equilibrium is established for the molar fraction XAl4C3/(Al4C3+SiC) < 0.5, which corresponds to the suitable condition for the Al4SiC4 condensation. Indeed, Al4SiC4 single phase could be experimentally condensed either by self-nucleation or as oriented film on SiC substrates.