In the method for growing large-volume monocrystals crystal raw material is heated in a melting vessel with heating elements to a temperature above its melting point until a melt is formed. A monocrystal is then formed on the bottom of the melting vessel by lowering the temperature at least to the crystallization point. A solid/liquid phase boundary is formed between the monocrystal and the melt. The monocrystal grows towards the melt surface in a direction that is perpendicular to the phase boundary. A vertical axial temperature gradient is produced and maintained between the bottom of the melting vessel and its upper opening and heat inflow and/or heat outflow through side walls of the melting vessel is prevented, so that the solid/liquid phase boundary has a curvature radius of at least one meter. A crystal-growing device for performing this process is also described.