The competitiveness evaluation of regional financial centers is frequently looked as the multiple attribute group decision-making (MAGDM) problem. Based on the TODIM method and fuzzy number intuitionistic fuzzy sets (FNIFS), this paper proposes a new FNIF-TODIM method to evaluate the competitiveness of regional financial centers. First, some basic theories related to FNIFS are briefly introduced. In addition, the weights of the attributes are obtained objectively using the CRITIC weighting method. Then, the traditional TODIM method is extended to FNIFS to obtain the final order of alternatives. As a result, all alternatives can be ranked and the best one for the competitiveness assessment of regional financial centers can be identified. Finally, an example for competitiveness evaluation of regional financial centers and some decision comparative analysis is listed. The results show that the established algorithmic approach is useful. The main works of this work are: (1) the paper constructs the FNIF-TODIM method for the evaluation of the competitiveness of regional financial centers; (2) the established method is illustrated by a case study for competitiveness evaluation of regional financial centers; and (3) some comparisons prove the rationality and advantages.