The present invention relates to providing a molten glass heating apparatus that heats molten glass such that no temperature difference occurs and suppresses an uneven quality of the molten glass. A molten glass heating apparatus (210) is provided with a composite pipe structure (220) provided with a main pipe (1) extending substantially perpendicularly to a horizontal direction, an upper branch pipe (2) branching from an upper side of the main pipe (1), and a lower branch pipe (3) branching from a lower side of the main pipe (1) and an energization heating unit (230) provided with an electrode (4) disposed in an upper end portion (1a) of the main pipe (1), an electrode (5) disposed in a lower end portion (1b) of the main pipe (1), and an electrode (6) disposed in a side end portion (2a) of the upper branch pipe (2), forming a first current supply path (21) for current supply between the electrode (4) and the electrode (5), and forming a second current supply path (22) for current supply between the electrode (4) and the electrode (6). The composite pipe structure (220) is configured such that the sum of the resistance of the current flowing between () the upper end portion (1a) of the main pipe (1) and an upper end portion Ja of a branch portion and the resistance of the current flowing between () a branch portion J of the upper branch pipe (2) and the side end portion (2a) divided by the resistance of the current flowing between () the lower end portion (1b) and the upper end portion (1a) of the main pipe (1) is greater than 0.4 and less than 0.8.