In this present, branched polyethyleneimine (BPEI)‐functionalized hexagonal boron nitride nanosheets (BNNS) were employed to improve the thermal conductivity and thermomechanical properties of epoxy resin. The 3‐glycidyloxypropyltrimethoxysilane (KH560)‐modified BNNS were firstly prepared via one‐step ball milling, and then reacted with BPEI to obtain BPEI‐functionalized BNNS (BPEI‐KH560‐BNNS). Results showed that, compared with neat epoxy resin, the thermal conductivity of epoxy nanocomposite filled with BPEI‐KH560‐BNNS increased by 189.8 % at 10 wt %, which is also higher than that of the epoxy nanocomposites filled with BN particles, BNNS and KH560‐BNNS. Besides, the highest storage modulus (3.23 GPa) and glass transition temperature (161.7 °C) were also achieved in 10 wt % BPEI‐KH560‐BNNS/epoxy nanocomposite, which increased 39.2 % and 20.9 °C respectively. This is mainly ascribed that the abundant amino groups on BPEI molecular chain can improve the interfacial compatibility and bonding strength between BN nanofillers and epoxy matrix, which has been observed in the morphology of the fracture surface of epoxy nanocomposites. This work provides an effective strategy for improving the thermal conductivity and thermomechanical properties of epoxy resin.