In this study, the novel ternary green polymer composites of poly(l-lactic acid) (PLLA)/poly(ethylene adipate)/hexagonal boron nitride (PLLA/PEA/h-BN) were synthesized and prepared. The crystallization rate of the biodegradable polymer PLLA in the composite was significantly increased with the addition of PEA and functional h-BN. In ternary PLLA/PEA/h-BN composites, PEA can be used as a plasticizer, while h-BN is a functional nucleation agent for PLLA. The analysis of the isothermal crystallization kinetics by the Avrami equation shows that the rate constant k of the ternary PLLA/PEA/h-BN composite represents the highest value, indicating the highest crystallization in the ternary composite. Adding h-BN in the composite can further increase the k value and increase the crystallization rate. Polarized optical microscopy (POM) images reveal that h-BN is an effective nucleation agent that increases the nucleation density of composites. Analysis of wide-angle X-ray diffraction (WAXD) further confirmed that the crystalline structures of PLLA were unchanged by the addition of PEA and h-BN. Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) images show that the h-BN particles are uniformly distributed in the composite. The distribution of h-BN having a particle size of a few hundred nm causes an effective nucleation effect and promotes the crystallization of the ternary composites.