The millimeter wave small cell backhaul network is one of the key solutions in 5G small cell backhaul. However, a lot of new challenges will be faced the multi-hop path planning is designed. In this paper, a flow network based energy efficient backhaul path planning algorithm (FBPA) is proposed for highly dense millimeter wave small cell networks so that the backhaul path planning with maximum throughput as well as minimum energy consumption is obtained. Firstly, the backhaul path planning problem is modelled as an integer programming (IP) problem, which is always a NP-hard problem. Then, a liner relaxation technique is used to make the problem be easier to resolve. Finally, the FBPA algorithm is proposed to find the path planning with minimum cost and maximum flow. Extensive simulations are conducted, the simulation results show that the backhaul throughput is improved by about 66.7% and energy efficiency is decreased by nearly 10% when the FBPA is compared to the existing path planning algorithm.