HMIPv6 (Hierarchical Mobile IPv6) protocol introduces MAP (Mobility Anchor Point) which relays all packets between MN (Mobile Node) and other nodes outside a MAP mobility management area. This method can reduce the amount of signaling traffic and improve handover frequency. Since very high loads are concentrated in a MAP and the load of MAP possibly influences the communication quality, the load balancing by suitable policy is needed in a multi-layered MAP network. This paper proposes load balancing with a 'score' calculated according to attributes of MNs, such as handover frequency and holding time. Simulation results showed that this proposed method could reduce the control traffic while achieving load balancing on multi-layered MAP in HMIPv6.