In this paper, dynamic load balancing with different quality-of-service (QoS) requirements is investigated in 3GPP long-term evolution (LTE) networks. Load unbalancing among neighboring cells often has different negative impacts on users with different QoS demands. For users with minimum rate requirements, the load unbalancing results in high new call blocking rate, while for users with no rate guarantees, the throughput of boundary users in an overloaded cell often significantly decreases. Furthermore, the different load unbalancing problems are coupled with each other so that it is difficult to analyze the problem in a uniform manner. To deal with this issue, a multi-objective optimization problem is proposed. The objectives in the problem are load balancing index of users with QoS requirements and the total utility function of users without QoS requirements, and the constraints are physical resource limits and QoS demands. Then the complexity of the problem is analyzed, and a real-time distributed algorithm framework with low complexity/overhead is proposed, which includes a QoS guaranteed hybrid scheduling scheme, handover of users with and without QoS requirements, and a call admission control algorithm. Extensive simulations are conducted and the results show that the proposed algorithm framework leads to significantly better load balancing so as to yield the decrement of new call blocking rate of users with QoS requirements, and the increment of throughput of boundary users with only a bit degradation of total throughput of users without QoS requirements.