Network Functions Virtualization (NFV) aims to support service providers to deploy various services in a more agile and cost-effective way. However, the softwarization and cloudification of network functions can result in severe congestion and low network performance. In this paper, we propose a solution to address this issue. We analyze and solve the online load balancing problem using multipath routing in NFV to optimize network performance in response to the dynamic changes of user demands. In particular, we first formulate the optimization problem of load balancing as a mixed integer linear program for achieving the optimal solution. We then develop the ORBIT algorithm that solves the online load balancing problem. The performance guarantee of ORBIT is analytically proved in comparison with the optimal offline solution. The experiment results on real-world datasets show that ORBIT performs very well for distributing traffic of each service demand across multipaths without knowledge of future demands, especially under high-load conditions.