The invention discloses a preparation method of a polylactic acid grafted copolymer. Polylactic acid is used as a raw material and reacts with a grafted monomer through a solid phase grafting method under the effect of an initiator. The preparation method is characterized by specially comprising the steps that the temperature of a reactor with a stirring function is increased to 60-90 DEG C, polylactic acid, the grafted monomer and the initiator are added in, stirring is carried out for 5-20 min, and a reaction is carried out for 1-3 h; the temperature is increased to 100-110 DEG C, and the reaction continues to be carried out for 0.5-1 h; the temperature is increased to 110-120 DEG C, the reaction continues to be carried out for 0.5-1 h, and therefore the polylactic acid grafted copolymer is obtained. The polylactic acid is grafted and modified through the solid phase grafting method, the grafting reaction is carried out in a solid powder shape or granular shape through the gradual heating mode, the reaction temperature is low, the reaction is easy to control, the product grafting ratio is high, and the prepared grafted copolymer not only has the interface capacity increasing effect, but also has the complete degradation performance, and can be used as functional polymer materials such as an interface compatilizer of polylactic acid based composite materials.