In this paper we address the problem of network contention between the migration traffic and the Virtual Machine (VM) application traffic for the live migration of co-located Virtual Machines. When VMs are migrated with pre-copy, they run at the source host during the migration. Therefore the VM applications with predominantly outbound traffic contend with the outgoing migration traffic at the source host. Similarly, during post-copy migration, the VMs run at the destination host. Therefore the VM applications with predominantly inbound traffic contend with the incoming migration traffic at the destination host. Such contention increases the total migration time of the VMs and degrades the performance of the VM application. Here, we propose a traffic-sensitive live VM migration technique to reduce the contention of migration traffic with the VM application traffic. It uses a combination of pre-copy and post-copy techniques for the migration of the co-located VMs (those located on the same source host), instead of relying on any single pre-determined technique for the migration of all the VMs. We base the selection of migration techniques on the VMs' network traffic profiles so that the direction of migration traffic complements the direction of the most VM application traffic. We have implemented a prototype of traffic-sensitive migration on the KVM/QEMU platform. In the evaluation, we compare traffic-sensitive migration against the approaches that use only pre-copy or only post-copy for VM migration. We show that our approach minimizes the network contention for migration, thus reducing the total migration time and the application degradation.