In a method and apparatus for evaporation depositing uniform thin films, a film is deposited on a substrate of a vacuum environment while maintaining a constant deposition rate. A cover is installed on a wall of the evaporation vessel. When the evaporation material is heated to an evaporation state and the interior of the evaporation vessel reaches a first vapor saturation pressure, the vapor of the evaporation material flows towards a pressure stabilizing chamber. When the pressure stabilizing chamber reaches a second vapor saturation pressure which is smaller than the first vapor saturation pressure, the vacuum environment has a vacuum background pressure which is smaller than the second vapor saturation pressure, so that the evaporation material vapor flows from the pressure stabilizing chamber towards the vacuum environment at constant rate due to the pressure difference, so as to evaporate the substrate.
