The development of the Internet of Things (IoT) plays a very important role for processing data at the edge of a network. Therefore, it is very important to protect the privacy of IoT devices when these devices process and transfer data. A mesh signature (MS) is a useful cryptographic tool, which makes a signer sign any message anonymously. As a result, the signer can hide his specific identity information to the mesh signature, namely his identifying information (such as personal public key) may be hidden to a list of tuples that consist of public key and message. Therefore, we propose an improved mesh signature scheme for IoT devices in this paper. The IoT devices seen as the signers may sign their publishing data through our proposed mesh signature scheme, and their specific identities can be hidden to a list of possible signers. Additionally, mesh signature consists of some atomic signatures, where the atomic signatures can be reusable. Therefore, for a large amount of data published by the IoT devices, the atomic signatures on the same data can be reusable so as to decrease the number of signatures generated by the IoT devices in our proposed scheme. Compared with the original mesh signature scheme, the proposed scheme has less computational costs on generating final mesh signature and signature verification. Since atomic signatures are reusable, the proposed scheme has more advantages on generating final mesh signature by reconstructing atomic signatures. Furthermore, according to our experiment, when the proposed scheme generates a mesh signature on 10 MB message, the memory consumption is only about 200 KB. Therefore, it is feasible that the proposed scheme is used to protect the identity privacy of IoT devices.