In IP-based mobile networks, a few of mobility agents (e.g., home agent, foreign agent, etc.) are used for mobility management. Recently, Hierarchical Mobile IPv6 (HMIPv6) was proposed to reduce signaling overhead and handoff latency occurred in Mobile IPv6. In HMIPv6, a new mobility agent, called mobility anchor point (MAP), is deployed in order to handle binding update procedures locally. However, the MAP can be a single point of performance bottleneck when there are a lot of mobile node (MNs) performing frequent local movements. This is because the MAP takes binding update procedures as well as data packet tunneling. Therefore, it is required to control the number of MNs serviced by a single MAP. In this paper, we propose a load control scheme at the MAP utilizing an admission control algorithm. We name the proposed load control scheme proactive load control scheme to distinct from the existing load control schemes in cellular networks. In terms of admission control, we use the cutoff priority scheme. We develop Markov chain models for the proactive load control scheme and evaluate the ongoing MN dropping and the new MN blocking probabilities. As a result, the proactive load control scheme can reduce the ongoing MN dropping probability while keeping the new MN blocking probability to a reasonable level.