The invention relates to step-by-step prepared grafted polypropylene with high melt strength, a preparation method therefor and use of the step-by-step prepared grafted polypropylene. The step-by-stepprepared grafted polypropylene is prepared from main raw materials, i.e., polypropylene, short-chain grafted monomer, a free radical initiator, silicone oil, peroxy acid or hydrogen peroxide and an antioxidant. Step-by-step preparation comprises the processing steps: (1) proportionally mixing the polypropylene, the short-chain grafted monomer and the free radical initiator in a high-speed mixer,subjecting the mixture to reaction extruding in a twin-screw extruder, and vacuumizing a die head of the extruder to remove ungrafted monomer, so as to obtain a short-branch-chain polypropylene graft;(2) subjecting the silicone oil and the peroxy acid or hydrogen peroxide to a reaction, and carrying out filtering and drying, so as to prepare termination epoxy group containing epoxy silicone oil;and (3) proportionally mixing the short-branch-chain polypropylene graft, the epoxy silicone oil and the antioxidant in a high-speed mixer, and subjecting the mixture to a fusion reaction in a twin-screw extruder, thereby obtaining the grafted polypropylene with high melt strength. According to the step-by-step prepared grafted polypropylene with high melt strength, the preparation method thereforand the use of the step-by-step prepared grafted polypropylene, the process flows are controllable, the product structure is neat, and the quality and processability are good.