In this study, the thermal percolation behavior for the thermal conductivity of nanocomposites according to the lateral size of graphene nanoplatelets (GNPs) was studied. When the amount of GNPs reached the critical concentration, a rapid increase in thermal conductivity and thermal percolation behavior of the nanocomposites were induced by the GNP network. Interestingly, as the size of GNPs increased, higher thermal conductivity and a lower percolation threshold were observed. The in-plane thermal conductivity of the nanocomposite containing 30 wt.% M25 GNP (the largest size) was 8.094 W/m·K, and it was improved by 1518.8% compared to the polymer matrix. These experimentally obtained thermal conductivity results for below and above the critical content were theoretically explained by applying Nan’s model and the percolation model, respectively, in relation to the GNP size. The thermal percolation behavior according to the GNP size identified in this study can provide insight into the design of nanocomposite materials with excellent heat dissipation properties.