Although industrial control systems (ICSs) recently keep evolving with the introduction of Industrial IoT converging information technology (IT) and operational technology (OT), it also leads to a variety of threats and vulnerabilities, which was not experienced in the past ICS with no connection to the external network. Since various control command messages are sent to field devices of the ICS for the purpose of monitoring and controlling the operational processes, it is required to guarantee the message integrity as well as control center authentication. In case of the conventional message integrity codes and signature schemes based on symmetric keys and public keys, respectively, they are not suitable considering the asymmetry between the control center and field devices. Especially, compromised node attacks can be mounted against the symmetric-key-based schemes. In this paper, we propose message authentication scheme based on double hash chains constructed from cryptographic hash function without introducing other primitives, and then propose extension scheme using Merkle tree for multiple uses of the double hash chains. It is shown that the proposed scheme is much more efficient in computational complexity than other conventional schemes.