Aminomethylpyridine grafted linear low density polyethylene (LLDPE-g-Py) was successfully prepared with 4-aminomethylpyridine and linear low density polyethylene (LLDPE), and then the modified BN/LLDPE (mBN/LLDPE) composites were prepared by melt blending. In the composites, due to the non-covalent action of LLDPE-g-Py and BN, the interfacial thermal resistance between filler and matrix is reduced, and BN is evenly dispersed in LLDPE matrix, so as to enhance the thermal conductivity of the composite. The thermal and mechanical properties of mBN/LLDPE composites were deeply studied. The results show that the thermal conductivity of mBN/LLDPE composites is greatly improved by the addition of LLDPE-g-Py, but too much LLDPE-g-Py will reduce its heat resistance. In order to improve the heat resistance of the composite, the LLDPE-g-Py mass fraction is fixed at 10%. When the BN mass fraction is 40%, the thermal conductivity of mBN/LLDPE composite reaches 0.95 W/(m·K), which is about 3 times that of pure LLDPE (0.32 W/(m·K)). At the same time, the tensile strength of mBN/LLDPE composites decreases slightly, and its elongation at break is significantly improved.