The invention discloses a preparation method of a heat shrinkable polyester film. The method comprises the following steps of: carrying out esterification and condensation polymerization reaction on multi-component dicarboxylic acid and multi-component dihydric alcohol in the presence of a catalyst, a stabilizing agent, an antistatic agent, a chain extender, an anti-caking agent or a modifying agent to prepare a multi-component polyester; carrying out melt extrusion, extension and pelleting on the multi-component polyester to prepare a multi-component polyester slice; and carrying out melted extrusion, die head casting, transverse far infrared drawing, cooling molding, rolling and cutting on the multi-component polyester slice to prepare the heat shrinkable polyester film. The heat shrinkable polyester film with high shrinkage percentage prepared by using the method is pretty high in strength and heat shrinkage performance, excellent in transparency, malleability, and toughness, good in glossiness, uniform in shrinkage, non-toxic, odorless, and easy to recycle, and a product of the film is suitable for labels for various containers and direct packaging of a food product, a beverage product, an electronic product, an electric product, a mechanical product, a hardware product and the like.