Thermally conductive composites comprising filler particles dispersed in a polymer matrix can effectively enhance the thermal conductivity (TC) by increasing the TC of the matrix; however, the TCs of polymers are difficult to increase. This study demonstrates that a liquid crystal polymer (LCP) that forms the matrix of a composite increases the TC to the value that is measured along the liquid crystal (LC) director orientation (λ // ). The LCP used here comprised a thiol−ene-type monomer that enabled grafting of the main-chain-type LCP onto allyl-functionalized magnesium oxide particles (MgOPs) with a diameter of 10 μm. The mixtures of LCP-grafted MgOPs and the LCP formed composite films with the MgOPs well dispersed in the LCP matrix at a MgOP volume fraction (v MgO ) of up to 34%. These films increased the TC up to 2.0 W m −1 K −1 as the v MgO increased, indicating that the LCP matrix increased the TC to 0.66 W m −1 K −1 . This matrix TC value was similar to the λ // value of the LCP (0.63 W m −1 K −1 ), suggesting that effective heat paths formed between the particles. These heat paths are associated with the matrix LCP aligning the director to follow the lines connecting the particle surfaces. This LCP director distribution was promoted by grafting LCP chains on the particle surfaces.