Internet of Things brings convenience to the social life, at the same time, putting forward higher requirements for the security of data transmission and storage. Security incidents based on industrial Internet of Things have occurred frequently recently, which should be given full consideration. The identity-based authenticated key agreement protocol can solve these security threats to a certain extent. Recently, a lightweight identity-based authenticated key agreement protocol for Industrial Internet of Things, called ID-2PAKA protocol, was claimed to achieve secure authentication and meet security properties. In this paper, we show that the ID-2PAKA protocol is insecure in identity authentication and cannot resisting ephemeral key compromise impersonation attack.