In Mobile IPv6, each packet sent and received by a mobile node contains its home address. As a result, it is very easy for an eavesdropper or for a correspondent node to track the movement and usage of a mobile node. This paper proposes a simple and practical solution to this problem. The main idea is to replace the home address in the packets by a temporary mobile identifier (TMI), that is cryptographically generated and therefore random. As a result, packets cannot be linked to a mobile node anymore and traffic analysis is more difficult. With our solution, an eavesdropper can still identify the IP addresses of two communicating nodes but is not able to identify their identities (i.e., their home addresses). Furthermore since a mobile node uses a new identifier for each communication, an eavesdropper cannot link the different communications of a given mobile node together. We show that HMIPv6 can also benefit from the proposed privacy extension.