In this paper, we propose a secure user authentication method for a networked manufacturing system, which is a system framework of computer-aided solutions to support the manufacturing industry, in particular the automobile and shipbuilding sector. The proposed authentication method called as CRI-TMT is based on a Challenge-Response Identification scheme using a Time-variant Mapping Table. The proposed CRI-TMT can prevent a user's secret from key-log or over-the-shoulder attack. Also a user's secret data is not stored on the verifier's side. Thus, a user's secret data is not disclosed even though attackers break into the authentication server. Through an analytical study, we show that the gain of the attackers who have users secret-related data by observing the verification step is not bigger than that of the blind attackers without any user's secret data. We also show the feasibility and practicality of the CRI-TMT system by a fast implementation.