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Failure mode and effect analysis (FMEA) is a powerful risk assessment tool to eliminate the risk and improve the reliability. In this article, a novel risk priorization model based on extended TODIM (an acronym in Portuguese of interactive and multiple attribute decision-making) method under interval-valued neutrosophic environment is proposed. Firstly, the interval-valued neutrosophic sets (IVNSs) are adopted to deal with uncertainty and indeterminate information. Secondly, in order to obtain objective weights of risk factors, integration of the new similarity degree and entropy measures are applied for risk factor weighting. Moreover, the extended TODIM method is present to reduce fuzziness in process of decision-making by using an improved score function, and it also attach importance to the psychological behavior of team members, which can get a more reasonable ranking. Finally, a numerical case of steel company is provided to illustrate the feasibility of the FMEA model, and a comparison analysis with other conventional methods are further performed to indicate its effectiveness.