A glass forming apparatus and a glass forming method are provided, which are capable of retaining the whole press surface at favorable temperatures for pressing glass, and forming a high-quality, efficient glass form. An upper die having a part formed such that the wall thickness of a bottom part, provided as an example of an opposite press surface, decreases gradually from the outside to the inside and the bottom part is formed as a part of the inner wall. In other words, the heat exchange chamber is in approximately a circular truncated cone shape.