Mobile IP is the current standard for supporting global mobility, however the performance degrades to support micro mobility. Cellular IP could be a good solution to accommodate efficiently hundreds of, thousands of mobile hosts that perform fast and frequent handoff in a small local area network. In semisoft handoff of Cellular IP, a mobile host sends a semisoft packet to the new base station before performing actual handoff to guarantee that the routing cache mapping associated with the new base station is created before actual handoff takes place. But packet loss and handoff delay are still occurred by this model. In this paper, we propose an advanced semisoft handoff method with no packet loss but with additional small packet delay just before or after handoff. In this method, the cross-over node calculates the time for the last message to be delivered to the mobile host via the old base station just before handoff based on four typical network models. On receiving that packet, the mobile host peforms handoff to the new base station. Our simulation experiment results show that the proposed semisoft handoff method actually outperforms the traditional semisoft handoff method in both handoff packet loss and handoff delay. We study the performance of the advanced semisoft handoff method with the network models.