Software-defined networking (SDN) decouples the control and forwarding of network devices, providing benefits such as simplified control. However, due to cost constraints and other factors, SDN is difficult to fully deploy. It has been proposed that SDN devices can be incrementally deployed in a traditional IP network, i.e., hybrid SDN, to provide partial SDN benefits. Studies have shown that better traffic engineering performance can be achieved by modifying the coverage and placement of SDN devices in hybrid SDN, because they can influence the behavior of legacy switches through certain strategies. However, it is difficult to develop and execute a traffic engineering strategy in hybrid SDN. This article proposes a routing algorithm to achieve approximate load balancing, which minimizes the maximum link utilization by using the optimal solution of linear programming and merging the minimum split traffic flows. A multipath forwarding mechanism under the same problem is designed to optimize transmission time. Experiments show that our algorithm has certain advantages in link utilization and transmission time compared to traditional distributed routing algorithms like OSPF and some hybrid SDN routing mechanisms. Furthermore, our algorithm can approximate the control effect of full SDN when the deployment rate of SDN devices is 40%.