A glass-melting furnace, which suppresses the effect of exhaust gas on molten glass quality, a process for producing molten glass, and a process and apparatus for producing glass products. The glass-melting furnace containing: a raw glass material particle feed portion disposed downwardly at a furnace wall portion in an upper portion of the glass-melting furnace; a heating unit provided under the feed portion, which forms a gas phase portion for converting raw glass material particles into liquid glass particles; a flue inlet disposed on the upstream side of the gas phase portion in a flow direction of the molten glass liquid; a furnace-bottom portion, which accumulates the liquid glass particles that produce the molten glass liquid; and a discharge portion, which discharges the molten glass liquid.