Mobile wireless sensor networks (MWSNs) are a new type of wireless sensor network (WSN) where sensor nodes are mobile. Compared to static WSNs, MWSNs provide many advantages, but the mobility introduces a problem of frequent reauthentication. To efficiently resolve this problem, several mobile node reauthentication schemes based on symmetric key cryptography have been proposed. However, most of the existing schemes do not preserve identity privacy of the mobile node and allow an adversary to track the movement of the mobile node. In this paper, we propose a pseudonymous mobile node reauthentication scheme for MWSNs that provides a mobile node reauthentication mechanism preserving the identity privacy of the mobile node. Furthermore, our scheme considers the node rejoin situation which was not considered in previous studies. By providing a simple reauthentication process for the node rejoin, our scheme reduces the energy consumption and latency in the reauthentication.