An ice-templating self-assembly strategy and a vacuum impregnation method were used to fabricate polyethylene glycol (PEG)/hierarchical porous scaffold composite phase change materials (PCMs). Hierarchically interconnected porous scaffolds of boron nitride (BN), with the aid of a small amount of graphene oxide (GO), endow the composite PCMs with high thermal conductivity, excellent shape-stability and efficient solar-to-electric energy conversion. The formation of a three-dimensional (3D) thermally conductive pathway in the composites contributes to improving the thermal conductivity up to 2.36 W m-1 K-1 at a relatively low content of BN (ca. 23 wt%). This work provides a route for thermally conductive and shape-stabilized composite PCMs used as energy storage materials.