A deniable authentication allows the receiver to identify the source of the received messages but cannot prove it to any third party. However, the deniability of the content, which is called restricted deniability in this paper, is concerned in electronic voting and some other similar application. At present, most non-interactive deniable authentication protocols cannot resist weaken key-compromise impersonation (W-KCI) attack. To settle this problem, a non-interactive identity-based restricted deniable authentication protocol is proposed. It not only can resist W-KCI attack but also has the properties of communication flexibility. It meets the security requirements such as correctness, restricted deniability as well. Therefore, this protocol can be applied in electronic voting.