It is a feasible way to use constructal filler to increase the effective thermal conductivity of polymer. However, the combined effect of filler constructal-shape, contact, anisotropy and interface thermal resistance on the effective thermal conductivity of the composites has not been considered, and the heat transfer mechanisms remain unclear. In this study, these effects are evaluated at the same time. The results show that the filler contact is a key factor in increasing the effective thermal conductivity of composite. The constructal fillers are easy to contact and form heat conduction network than common filler. The filler content of 5 % is the percolation threshold of constructal filler. It is lower than common filler and previous reports. The enhanced heat transfer performance of constructal filler is insensitive to directional angle and has no significant anisotropy. The composite with constructal filler has high effective thermal conductivity in different directions. Series numerical models are proposed to predict the effective thermal conductivity of composite. These models have high accuracy and reliability, the deviations with experiment results is in an acceptable range. The interface thermal resistance should be considered in predicting the effective thermal conductivity of composite with nano-fillers.