The most common non-granular fillers are sheet and fiber. When they are distributed along the heat flux direction, the thermal conductivity of composite increases greatly. Meanwhile, the filler contact also has large effect on the thermal conductivity. However, the effect of filler contact on the thermal conductivity of composite with directional fillers has not been investigated. In this paper, the combined effects of filler contact, content and orientation are investigated. The results show that the effect of filler orientation on the thermal conductivity is greater than filler contact in low filler content, and exact opposite in high filler content. The effect of filler contact on fibrous and sheet fillers is far greater than cube and sphere fillers. This rule is affected by the filler contact. The filler content of 8% is the ideal percolation threshold of composite with fibrous and sheet filler. It is lower than cube filler and previous reports. The space for thermal conductivity growth of composite with directional filler is still very large. The effect of interfacial thermal resistance should be considered in predicting the thermal conductivity of composite under high Rc (>10-4).