Graft copolymers have unique application scenarios in the field of high-performance thermoplastic elastomers, resins and rubbers. β-myrcene (My) is a biomass monomer derived from renewable plant resources, and its homopolymer has a low glass transition temperature and high elasticity. In this work, a series of tapered copolymers P(My-co-AMS)k (k = 1, 2, 3) were first synthesized in cyclohexane by one-pot anionic polymerization of My and α-methyl styrene (AMS) using sec-BuLi as the initiator. PAMS chain would fracture when heated at high temperature and could endow the copolymer with thermal degradation property. The effect of the incorporation of AMS unit on the thermal stability and glass transition temperature of polymyrcene main chain was studied. Subsequently, the double bonds in the linear copolymers were partially epoxidized and hydroxylated into hydroxyl groups to obtain hydroxylated copolymer, which was finally used to initiate the ring-opening polymerization (ROP) of ε-caprolactone (ε-CL) to synthesize the graft copolymer with PCL as the side chain. All these copolymers before and after modifications were characterized by proton nuclear magnetic resonance (1H NMR), gel permeation chromatography (GPC), thermogravimetry analysis (TGA), and differential scanning calorimeter (DSC).